It was the best of times, it was arguably not really the worst of times. Either way we once again have football public relations to thank for a tale of two cities. In Manchester we have Manchester City, whose enjoyable and interesting fly-on-the-wall Amazon documentary has received almost nothing but plaudits.

Despite the series having been quite clearly subject to a form of copy approval by the club, City have been praised for their “risk-taking”. The results have been described as “not sanitised” in the Daily Mail, which was presumably still high on the Dettol fumes. I note one particular guy in Manchester did not much care for it but in general it went over as you might expect of a high-access documentary about a normally low-access obsession.

'Back to the middle ages': Italian police investigate Lazio fans' sexist flyers Read more

In Rome, meanwhile, the Lazio ultras are operating on slightly less of a PR budget but they absolutely refuse to be held back by it. To this end the Irriducibili group has put out a flyer telling women to stay away from their section of the Stadio Olimpico, calling it a “sacred space”. I’ll spare you the full thesis but it goes: something something “we do not allow women, wives and girlfriends”, something something “experienced like the trenches”.

This no-budget act has earned them approximately 20 miles of global column inches (20 miles 4 inches after this), and plenty of broadcast coverage. Either this scrap of leaflet gets denounced by pundits keen to make the point that banning women from places is bad or it gets denounced by various Lazio proxies, who say this is nothing to do with the club.

I particularly enjoyed the Italian gentleman whom the Today programme appeared to have sourced from central casting and whom it was impossible to hear without imagining the arm gestures he would have been making as he naughtily refused to take it very seriously and batted away questions with airy rejoinders such as “you have never been there, my friend”.

In general UK media outlets have been obligingly outraged that women should be denied, in a non-formal manner, the opportunity to sit with the chaps whose wide-ranging racism is occasionally the reason no one at all is able to sit anywhere in the Stadio Olimpico and watch Lazio play.

I don’t wish to speak for the ladies of Rome but I imagine being told you can’t sit in the calcio Somme is a little like being told you can’t attend two hours of men’s rights performance poetry – upsetting, of course, but you get on with your day as best you can. The Italian FA has now opened an investigation. I myself thought about opening a joke about Italian FA investigations but have immediately closed it.

Not for the first time, then, the Irriducibili’s PR gambit has proved that a little goes a long way. But a lot goes even further and we must marvel at City’s continuing ability to suggest there are Chinese walls between the club and the regime that owns it. The eight-part documentary/product/piece of content diversification is the latest play in the emirate’s stunningly fast-tracked acquisition of soft power and influence.

Facebook Twitter Pinterest All Or Nothing gave viewers a behind-the-scenes view of Manchester City. Photograph: Amazon Prime

We can all see that football in the modern era is a vehicle for reputation laundering. Only last month Gianni Infantino dismissed the idea the World Cup had become a way for morally challenged regimes to launder their reputations. Mere moments later the Fifa president explained: “This World Cup certainly did change the perception of the world towards Russia. It changed a lot of pre-conceived opinions.” That’s the trouble – it is such fun to watch the laundry being done that it is easy to forget what caused the stains.

And so with club ownership, Abu Dhabi style. The emirate’s rulers are hardly in it to make money and no one could accuse them of being especially interested in football. All the all-access documentaries in the world should not distract from the fact City’s owner is part of a regime of ghastly autocrats, and every attempt to misdirect attention away from that – no matter how pretty – is an action performed in that regime’s service. As the regional human rights expert Nicholas McGeehan has put it: “While Abu Dhabi may not be the most abusive government in the world, they are easily the most abusive government running a football club.”

I’m not remotely suggesting people switch off City, widely acknowledged as among the most wonderfully watchable sides in the world. But we don’t always have to fall quite so completely for their owners’ sleight of hand. Trying not to look the wrong way is the very least we can do. This week those concerned about the sharp end of women’s rights would have been rather better off not rising to the Lazio ultras’ bait and focusing instead on the disconnect between an ultra-modern and attractively successful Premier League club of that documentary – one that spouts all the right things about equality and diversity and so on – and the oppressive regime that pays for it all.

There is no space for a full rundown of the contrasts but by way of a flavour: UAE husbands are allowed to beat their wives; marital rape is not a crime; hundreds of rape victims are flogged or imprisoned every year under laws prohibiting extra-marital sex … it goes on and on.

Are these bigger issues than the unofficial seating arrangements for Lazio games? Not so as you’d notice from the coverage.