Oliver Stone looks overwhelmed. It is May 2015, and we are in Munich on the penultimate day of shooting his drama about Edward Snowden. At lunch, the director seems anxious and weary, eyes heavy, shoulders stooped, energy sapped. When the idea of Snowden was proposed, he explains, he had strongly resisted. Then, slowly and reluctantly, he was drawn in. Today, he sounds as if he might regret that decision. There have been problems with finance, with finding distributors, in portraying something as dull as the cyberworld that Snowden inhabits.

“A director has to say everything is great, things are wonderful,” he says, exasperated. “Every day on a set is a potential disaster. Every day on a film set is the hope that it is turning out well, but the truth is it is just a slog all the way through. It’s the bulldozer going through a treeline. It is not easy. It has never been easy.”

This film, in particular, was not easy. “Every movie I have made is a challenge. But from day one, every day seems to have its obstacles, whether it is computers or the technology being arcane, difficult to understand, or the character of Snowden, who has a strong, robot, nerd quality. It is a drawback. He is not the active type.” As Stone headed back to the set, his final comment expressed his limited ambition for the movie at that time: “I don’t want to do anything that will hurt Edward Snowden.”

Almost a year later, I meet Stone again, in London. The tiredness is gone. This is a man full of enthusiasm for life and his movie. The editing has gone well, he feels; the previous week a positive reaction had met an early preview in Idaho – despite his sense of dread.

“As a director, I think the film has a power beyond its details,” he says, beaming. “Maybe no one will come. But those people that come will see something they have not seen before. There are no chases. There are no murders. I love tension but there is a different kind of tension … What Snowden did in history, I believe, will make a difference. I don’t think it is going to go away.”

It was a few months after the story first broke in summer 2013 that Stone was approached by Anatoly Kucherena, Snowden’s lawyer in Russia, about making a movie about his client. It caught him, he says, at a low point. A project about Martin Luther King had failed to come to fruition. He didn’t fancy embarking on another complicated proposition unlikely to make it to the multiplex. Nonetheless, he went to Moscow, met the man himself, and was sufficiently intrigued to do further research and buy up film rights to Kurcherena’s fictional account of an American whistleblower, Time of the Octopus, as well as Guardian correspondent Luke Harding’s The Snowden Files.

I first met Stone six or so months later, when he visited the Guardian. I was called into the office of the then-editor, Alan Rusbridger, and was pleased at the prospect, never having met a Hollywood director before. This was also one whose films I had enjoyed. There were a handful of us in the room and we chatted for about hour. The reason I was there was that, along with fellow journalists Laura Poitras and Glenn Greenwald, I had met Snowden in Hong Kong, where he handed over tens of thousands of top-secret US and British documents to us – one of the biggest leaks in intelligence history – before going into hiding. Stone wanted to hear the account firsthand. At that point, I wasn’t sure what to make of the director, but I was impressed by the detail he had already accumulated about Snowden.

Oliver Stone on the set of his film Snowden. Photograph: Jürgen Olczyk

I met him next in December 2014, alone over lunch in London. I was half-an-hour late but he did not make a fuss: there was nothing of primadonna to him. Instead, he cracked on with his questions. There were a lot of them. They were followed up with emails and phone calls. I liked this obsessiveness, more journalist than film director; a stubborn pursuit of the unanswered in an effort to complete a picture. In the end, Stone and his co-writer Kieran Fitzgerald interviewed almost everyone involved. He spoke to lawyers, journalists and former members of the NSA. He went to the Ecuadorean embassy in London to talk to WikiLeaks founder Julian Assange. And he met Snowden’s partner, Lindsay Mills. He went to Moscow at least eight times to meet Snowden.

Too much research, Stone says. About 80% had to be ditched. Not time wasted though, he says – it gave him the clarity he hankered after. We are now back in Munich, two days after the UK general election: a time of great industry and excitement in a newspaper. Filming, by contrast, is boring. I had never been on a movie set before and I am glad I had the chance to see behind the scenes. But I had somehow imagined it might be a bit like a stage performance. It was not. The experience is dull and repetitive. That morning was dominated by Stone shooting Joseph Gordon-Levitt, who plays Snowden, looking out of a hotel window. This was meant to be in Hong Kong; Snowden’s bedroom at the Mira hotel having been recreated in Germany. Gordon-Levitt was filmed looking left to right and then down to the street. Over and over again. Different lighting. Different angles. Different shots. The scene makes it into the movie but only lasts a few seconds. It took four hours.

When not looking out of glass, Gordon-Levitt was happy to chat. By then, he had already met Edward and was accurately reproducing his slow, precise speech. The son of west coast liberals, he had fostered an intense interest in Snowden and the arguments around surveillance. Unafraid of public declarations of political intent, Gordon-Levitt was preparing to be an advocate for privacy issues in the press commitments ahead. He has already donated his earnings from the movie to the American Civil Liberties Union, one of whose lawyers is Snowden’s chief representative.

Watching the shooting in the mocked-up Hong Kong hotel, I spotted on Snowden’s cluttered table an empty can of Tsingtao beer. But there were never any empties in that room. None of us was drinking at the time; Snowden is teetotal. But I didn’t have the heart to mention it because it was already so far into the shooting and the idea of subjecting them to more hours reshooting felt unimaginable. In the end, though, I can’t remember seeing the stubbie in the final cut.

There are other, bigger quibbles. Parts of the film are pure Hollywood. Stone devotes much of the movie to the romance between Snowden and Mills. The way Snowden smuggles data out of the NSA headquarters in Hawaii in a Rubik’s Cube is almost certainly the stuff of thriller fantasy. It is also a straightforward biopic, following Snowden from a failed attempt to join US special forces to a successful career as an NSA computer specialist, through disillusionment and then to being a whistleblower.

Yet the broad direction of Snowden is more faithful to the truth than might be expected from Hollywood. Stone is quick to insist he is not a political director or an activist, but a dramatist. A surprise to me, maybe to others also familiar with his work. Yet perhaps what he meant was that he does not want to make anything that would be dull. The film isn’t. But I’m an interested party: I’m depicted in it, and so I hope it does well.

I’m most interested in the film’s capacity to shift public opinion about the man whose story it portrays. Attitudes in the US tend to be polarised between those who view him as a traitor and those who see him as a hero. Stone’s film can reach people with little prior knowledge. It humanises its subject, makes complex arguments about the balance between privacy and surveillance immediately understandable. Even those who argue that they are not bothered about potential intrusion into the private lives will likely squirm at a scene in which the central couple are having sex – but then Snowden hesitates, spotting an open laptop, wondering if anyone might be watching through the webcam. (The incident is based on an interview with the Guardian in which Snowden said surveillance agencies do engage in such voyeurism.)

Joseph Gordon-Levitt as Edward Snowden and Shailene Woodley as his girlfriend Lindsay Mills in Snowden. Photograph: Allstar/Open Road Films

Will Snowden shift opinion? “I hope so,” Stone says, a touch uncertain. “It is tricky,” he qualifies. In fact, his film may give some of the more zealous anti-surveillance campaigners pause for thought. One of the more unexpected subtleties in the film comes with its portrayal of the NSA, where differing views about the balance between privacy and security are permitted – embraced, even.

“Ed never revealed real people to us,” said Stone. “But he gave us ideas about real people and events from which we could draw and make – with dramatic licence – conclusions that would not be too far-fetched. We tried over many drafts to make it as realistic as possible.

“The NSA have human souls,” he added. “They are not all James Bond villains.” He was not smiling; he meant it.

Yet his own allegiances lie with the whistleblower; his undoubted aim is to caution the unaware about what he calls “the surveillance state”. “I think we are all facing problems of an Orwellian super–organisation that is running the world,” he says. “But that is politics!” He is disappointed that the issue has surfaced so little in the US election campaign so far – its sole appearance at that point was in a Democratic candidates’ debate. Stone backed Bernie Sanders (and is also a fan of Jeremy Corbyn). “Hillary Clinton has no mercy in her soul for Snowden,” he says, also murmuring uneasily about her “hardcore warmongering tactics”.

Snowden will be released in the US two months before a new president is elected, and a day after Stone’s 70th birthday. Its fate will be decided then. But what of the most important opinion, that of Snowden himself? His instinct when he worked at the NSA was to keep a low profile – presumably he would have been mortified at the prospect of a movie about him. And he remains an essentially private person, happy to talk about technology and surveillance, but guarding details about his own life. The world of the celebrity is not one he would be comfortable with.

Stone hints that Snowden liked the movie – and his cooperatation suggests he is onside. His real pleasure in it, though, may be like mine. In April, the trailer was released. Snowden tweeted: “For two minutes and 39 seconds, everybody at NSA just stopped working.”

His accent is good, if more Edinburgh than my Glasgow glottal stop

Ewen MacAskill meets Tom Wilkinson, the man who plays him in Snowden

Tom Wilkinson as Ewen MacAskill in Snowden. Photograph: Allstar/Open Road Films

After seeing the Oscar-winning movie Citizenfour, a Guardian colleague offered up his verdict: “The guy playing you is rubbish.” It was a joke, I hope; the guy playing me is me, as Citizenfour is a documentary.

Released in 2014, Citizenfour recorded a meeting between NSA whistleblower Edward Snowden with three journalists, Laura Poitras, Glenn Greenwald and myself, in Hong Kong in 2013. Oliver Stone’s Snowden is different. Actors take most of the roles, including Tom Wilkinson as me.

Throughout my career, I have been comfortable with a low profile, hiding behind print. That has not survived the Snowden story, which has so far spawned three plays, several documentaries and now a Hollywood movie.

My part in all of them is relatively small. Even so, the first time I went to see myself played by an actor – Jonathan Coy, in James Graham’s Privacy at the Donmar Warehouse in 2014 – I felt a mixture of both embarrassment and dread, not least because I had to write about it. But Coy did a good job and I began to relax after he delivered the first of his lines. I had met the actor before on what I thought was a social occasion – in fact, he was scoping me, picking up mannerisms.

It gave me a strange taste for this strangest experience. When I flew to Munich to visit the set of Snowden, two things were uppermost in my mind. The first: would my small role survive the final cut? The second: would I keep my Scottish accent? Stone might have opted for American, or even English.

In a break on set during a thunderstorm, I met the man playing me: Tom Wilkinson. He confirmed he stuck with Scottish. “It is always an accent I have never had any problems with,” he said. “I am good with accents in a way and Scottish is apparently one of them.” And his accent is good, if a little more Edinburgh than my Glasgow glottal stop. Plus, he refers to Snowden in the movie as “laddie”. Not a term I would ever employ.

One of the biggest differences between being portrayed on stage and on film is that the language in the play was mine, recorded verbatim, while that in Snowden is invented.

At one point in the real meeting in the Mira hotel, Snowden covered himself and his laptop with a red hood. He wanted to hide his password from any hidden cameras, he explained later. Even at the time it seemed odd behaviour and myself and Glenn are caught in Citizenfour exchanging puzzled, uneasy glances.

In the movie, I offer up a quip as Snowden pulls the hood over his head, something like, “Do we all get under that?”, which I did not say. Stone repeatedly stressed to me he was making a movie and had to make it interesting. Me just taking notes in a chair, he said kindly, just wasn’t particularly exciting. He needed action.

There’s another striking line in which I call the Guardian to tell them that “The Guinness is good” – a pre-arranged signal that the whistleblower was genuine, not a crank. In fact, I did say that in real life. And, oddly, it was scripted, the brainchild of then-Guardian US editor Janine Gibson, who is played here by Joely Richardson.

The film shows me nodding off. This is accurate, too – but it happened later than the scenes shown. Neither Glenn, Laura or myself got much sleep for a week. It was only when Snowden went into hiding that I began to relax and started falling asleep all over the place.

As for Wilkinson, he was less exercised by the themes behind the film than his director or co-star, but he recalled with excitement the coverage in the Guardian when the story broke, and is sympathetic towards the man. “I don’t think he is a traitor,” he says, quiet and considered. “You need someone like that. I think all people who put themselves out on a limb to the extent to which he has have a simplicity of outlook that eludes the rest of us.”

Earlier in the summer, I saw a preview of the film with my colleague Luke Harding, on whose book much of the movie is based. Afterwards, I asked him how accurate he felt the Wilkinson portrayal was. A fearless foreign correspondent confronting the powerful forces of the US and British intelligence services – right? Luke’s verdict: “You looked a bit dopey.”

• Snowden premieres at the Toronto film festival on 10 September, opens in the US on 16 September and in the UK later in the year