It is almost forgotten now what a decisive role Sweden played in the Vietnam war. Even at the time, the armies doing the fighting and the million or so Vietnamese doing the dying may have underestimated the importance Swedish public opinion had on their struggle. But in Sweden it was never in doubt. The starting point for this weird, sad, horribly readable story is the arrival in Stockholm in May 1968 of six misfit and confused US deserters from the Vietnam war after they had been shepherded across the Soviet Union from Japan, where a fishing vessel had smuggled them on to a Russian ship.

They had been transported across the USSR “on a current of vodka” and with women supplied by the KGB; they had even been questioned by Yuri Andropov, later to rise to supreme power, and helped to make a propaganda film in which one of them, according to Sweet’s account, who had been a ship’s cook and never landed in the country, gave wrenching testimony of all the atrocities he and his unit had committed on the ground in Vietnam.

To progressive Swedish opinion at the time they were a demonstration of the country’s stand as a moral beacon for the world. This was only six years after the death of Dag Hammarskiöld, the Swedish secretary general of the UN. The country still thought of itself as the spearpoint of human progress. What the deserters made of it is rather harder to tell.

They seem to have had as little as possible to do with their Swedish hosts, except for the girlfriends they rapidly acquired. There were already around 80 deserters in Sweden and the kind of high-minded patricians who had originally tried to help them were relegated to the status of useful idiots. Although Matthew Sweet gives a vivid account of the group’s arrival at Arlanda airport, where they gave a press conference after expelling all the US press and wire services, I can find no trace of this in contemporary Swedish newspapers. The story comes from the memoirs of one of the most resourceful of the group (and the only black man), Terry Whitmore, but the archives of the two Stockholm morning papers record instead that the men were driven straight from their plane to a police station, where they were held over the weekend while their papers were processed.

The Vietnam Memorial in Washington DC. Photograph: Alamy

On the Monday, Bertil Svahnström, a distinguished former foreign correspondent and pacifist who ran the Swedish Vietnam Committee, had arranged a press conference. But the men never turned up. They had been driven away by the American Deserters Committee, an organisation whose funding, purposes and animating spirits are all shrouded in mystery. Svahnström was left apologising to the media. There is no contemporary record of the press conference that the book describes, either at the airport or anywhere else.

The difficulties of establishing even such a simple fact as when and where the deserters first spoke to the Swedish press supply only a foretaste of the puzzles that Sweet explores.

The American Deserters Committee was of course infiltrated by the CIA, as well as by the Swedish security services and presumably the KGB as well. The survivors Sweet has tracked down all believe they know who the spies were, and all disagree. Most of the explanations are plausible. Certainly they are far more plausible than the undisputed reality, which is that the core of the group who went to Stockholm fell into the clutches of an American fantasist and convicted fraudster, who built a cult that endures to this day.

Lyndon LaRouche. Photograph: Shepard Sherbell/Corbis/Getty Images

Cliff Gaddy, a deserter who reinvented himself as an expert on Vladimir Putin at the Brookings Institution, a respected Washington thinktank. But none of them, not even Gaddy, are as unlikely as Lyndon LaRouche, the self-taught Marxist who swept many of the deserters into his cult, and ended up running for president of the US eight times in a row.

The LaRouche cult was violent and paranoid. In the terminology of Dungeons and Dragons – a game whose worldview is rather more realistic – its alignment was chaotic evil. Sweet describes a cult that taught, and teaches, that the British empire is the greatest force for evil the world has ever known and that the Queen, Henry Kissinger and Olof Palme, the assassinated prime minister of Sweden, are figures of transcendent wickedness. Half a dozen deserters were swept up inside it and many remained there for decades.

I’m not sure that this was the intended effect, but I finished reading Operation Chaos with a bewildered admiration for the unhappy spooks whose job it was to make sense of the people they spied on.

• Operation Chaos: The Vietnam Deserters Who Fought the CIA, the Brainwashers and Themselves is published by Picador. To order a copy for £17 (RRP £20) go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.