The Winter Olympics in Sochi have given western journalists no end of fodder for outrage and absurdity – at the cost of accuracy. Despite the just concern about gay rights and entertaining tweets about Sochi’s half-built hotels, a number of persistent stories about Russia and its dissidents could use a little clearing up.

To that end, consider the following …

1. Vladimir Putin probably doesn’t care about LGBT rights, one way or another

As plenty of astute observers have noted, Putin doesn’t tailor domestic policy to international demands. Russia’s gay community, like its immigrant community, is being used as a scapegoat in an attempt to quash domestic dissent. By pointing fingers, to distract and divide, Putin has tried to defuse urban protests against him and rally his conservative supporters.

First up were the Americans (remember when he blamed Hillary Clinton for protests?) and despite his hard work, Ambassador Michael McFaul has become the fall guy for strained US-Russian relations. Then the government targeted immigrants, most non-ethnically Russian, and violent riots broke out between nationalists and immigrants. Finally, the LGBT community landed in legislators’ sights, largely because it fits with religious discomfort over gay rights – religion is a powerful card in Russia, bound up with national identity. Russia’s anti-LGBT laws are more a political card than a symptom of Putin’s own bigotry. His government, which only concerns itself with power, is encouraging bigoted Russians.

1a. These aren’t unfamiliar tactics. American and British politicians have stirred up xenophobia for centuries and the culture war over same-sex marriage, even after a breaking point in the US supreme court last year, continues across the US. But American and British laws protect minorities as equal citizens, while Russian courts routinely circumvent the law as needed, and police corruption means minorities cannot expect safety.

1b. Though Putin signed the provocative anti-LGBT bill into law, he never overtly instigates violence arising from it. Rather, his supporters in the Duma (Russia’s parliament) propose plans, and he approves or freezes them. As Peter Pomerantsev brilliantly describes, Putin’s crony politics grew into what Russians call “the System”, which runs on corruption so pervasive that it implicates even those who would resist it. Of course, this system is also why Sochi has famously cost so much, and why journalists’ hotels were not a priority.

The point here is that it’s not just Putin. A massive system of corruption allows hate and violence to persist against gay people, non-white people and even women and foreigners. The blame lands most on Putin, but the System includes any number of power players (siloviki), petty bureaucrats (chinovniki), complicit businessmen (the infamous oligarchs) and corrupt cops. This is why Putin’s nemesis, Alexei Navalny, won fame for his anti-corruption efforts, and why Putin has a weird tic of being pathologically averse to saying Navalny’s name.

2. Pussy Riot isn’t a band

Madonna introduces Maria Alyokhina and Nadezhda Tolokonnikova at an Amnesty International concert in New York. Photograph: Jason Szenes/EPA

At least not in the sense of a band which sings songs and plays music, it’s not. As a group of art-collective dissidents, sort of Robin Hood merry, anti-capitalist feminists – sure, you can call them a band.

Pussy Riot is a political art group with punk and Slavoj Zizek as philosophical touchstones. It split off from a street art group called Voina (War), which has painted phalluses on drawbridges and staged an orgy in a museum (Nadezhda Tolokonnikova, before her political prisoner fame, took part). When members in Russia say Tolokonnikova and Masha Alyokhina aren’t Pussy Riot, they’re clarifying something that has long been obvious.

In their infamous cathedral performance, you’ll notice that they’re not playing instruments – they’re simply shouting political verses. Tolokonnikova and Alyokhina have even said they’re not in a band, and that they’re now fighting for the rights of political prisoners – an admirable and daunting goal, especially given the harrowing time in prison they have endured. But they’re not going to sing about it.

2a. Westerners should rightly feel outraged about Russia’s crackdown on free speech, but should also keep perspective about why Pussy Riot is controversial at home. Russia is by and large a very conservative country and religion is almost untouchable, politically. This should also sound familiar. Imagine how Catholics might feel if people in ski masks ran into St Peter’s and shouted about cardinals’ ties to Berlusconi, or if protesters disparaged Saudi Arabia’s treatment of women’s rights in a major mosque. When was the last time you heard a US president criticize Christianity?

Tolokonnikova and Alyokhina have expressed regret about offending Orthodox Christians, and made clear that their trial was reprehensible because it showed how Russian’s vague “hooliganism” law can be bent to prosecute anyone for anything.

3. Putin’s big amnesty wasn’t just a PR move

The Olympic rings in Sochi. Photograph: Fabrizio Bensch/Reuters

It was another domestic ploy. As noted, Putin cares about international politics insofar as he can use them – Exhibit A being the clever way he brokered half-measures over Syria and its chemical weapons. Those negotiations let Putin have it both ways: he kept a military strike off Bashar al-Assad and he got to play peacemaker against a would-be hegemonic US. It’s a story Putin wants to sink in.

The amnesty deal, like the Syria talks, lets Putin have his cake and eat it: by forgiving his opponents, he disarms some criticism while also keeping the status quo (protesters are still being prosecuted). Because of the crony system, Putin can say that he’s forgiving people who were rightly convicted by a justice system that acted independently of him. Meanwhile, he puts freed prisoners in the awkward position of being in his debt, always aware that they could go back to prison.

Of those released, only Mikhail Khodorkovsky, an ex-oligarch who served almost a decade behind bars, poses a credible political threat to Putin. Immediately after his special pardon, he left the country. As far as Putin is concerned, these prison sentences served their purpose (to punish and intimidate), and pardons are the natural conclusion of the play. He using false generosity to assert control and political flexibility.

4. Russians are hunting dogs all over the country

Unfortunately, gangs have been killing strays for several years now – it’s not just the government contracting a pest control service in Sochi. The good news here is that lots of Russians are also outraged, and are working to stop it.

5. Russia won’t let Americans eat yogurt

OK, this one probably is just a petty way to mess with Americans, especially US senator and part-time yogurt salesman Chuck Schumer, who is angry that athletes have been kept from receiving this “nutritious and delicious food”.

6. Sochi’s hotels, services and infrastructure are a mess

As countless reporters’ tweets attest, this is true. As the New Republic’s Julia Ioffe thoughtfully counters, though, this is beside the point and verging on schadenfreude. Given collapsing bridges and power outages in cities that weren’t built by the will of one man, the US should probably get its own act together.

7. Sochi matters to Putin because of his bad record on terrorism

Police patrol outside the Olympic Park. Photograph: David Goldman/AP

Amid all the talk of these Olympics as Putin’s baby, legacy and dacha by the sea, there is a deeper narrative at stake: stability v chaos.

Putin’s won his first election on the promise that he would end the strife and economic madness of the 1990s, and over the past 12 years he’s done that – at the price of corruption and authoritarianism. The wars in the Caucasus, a region that abuts Sochi, were largely won by Putin during a long and bloody campaign, but his use of warlords (eg: the terrifying and absurd Ramzan Kadyrov in Chechnya), has apparently only diffused extremism.

As Christian Caryl argues, this makes Sochi a powerful symbol of 90s chaos versus Putin’s dysfunctional peace today. The theater of the Olympics is a way for Putin to sell himself to the world as Russia’s triumph, and also to Russians feeling ambivalent about another 10 years of his presidency.

But terrorism in Putin’s Russia is real and storied, from the theater hostage crisis in 2002 to the Moscow metro bombings in 2010 and the Volgograd bombings last December. Despite the sweeping measures Putin has taken, warlords, secret police and the System have proven tenuous protections at best. Sochi is a chance to show off that these tactics do work, and by extension that Putinism, despite its $51bn price tag here, also works. Putinism doesn’t work, of course, but because everyone wants a safe, triumphant Olympics, everyone has to root for Russia while figuring out ways to protest its practices.

In other words, Russia matters whether the world likes it or not, and it will keep finding ways to matter. For every stereotype that fits the bill, there’s another that defies it. Russia is a strange, remarkable country that’s endured horrific wars and oppression while also creating some of the world’s greatest achievements in art and science.

It has produced Chekhov, Tchaikovsky and a men’s police choir singing Daft Punk. It’s complicated, so let’s treat it that way.