The band's screeching, discordant guitars and jarring, garbled vocals would be few people's favourite cup of Russian caravan tea. However, the overwhelming perception in the West - given oxygen by such high-profile figures as Madonna and Sir Paul McCartney - is that Pussy Riot have been persecuted because of growing restrictions in Russia on freedom of expression and speech.
For many in the West, the plight of the three jailed band members has come to symbolise everything wrong with Putin's third presidential term.
In the process, Pussy Riot have shot to international fame at a speed not seen since Malcolm McLaren's Sex Pistols in the 1970s.
The recipe is the same - highly provocative behaviour producing mass public outrage, thereby prompting the authorities to overreact.
In the Pistols' case, it began with a few swear words on live television. Pussy Riot's mask-wearing performance of their anti-Putin and profanity-ridden "Punk's Prayer" on the altar of Moscow's Cathedral of Christ Our Saviour was something else altogether.
Polling shows most Russians - especially Russian Orthodox believers - approving of the subsequent charges of hooliganism and incitement of religious hatred brought against those band members whom authorities were able to identify from videos of the performance.
The pro-Putin media duly fell into line. The Pravda newspaper referred to the "miserable meeowing"of Pussy Riot, while another tabloid screamed "Unholy Madonna" after the American superstar denounced the sentences as "inhumane".
The subsequent shift to damage control saw the foreign ministry stressing the independence of the Russian judiciary and noting there are curbs on freedom of expression in the International Covenant on Civil and Political Rights.
Russian Foreign Minister Sergei Lavrov has, meanwhile, been trawling through other European countries' law books and finding plenty of examples of similar jail terms for crimes of blasphemy.
Whether those countries ever seek recourse to those laws is a moot point. Moscow, however, views what Lavrov labelled as international "hysteria" over Pussy Riot as another case of the West's double standards.
The Russian media has focused far more than their Western counterparts on past performance art undertaken by Pussy Riot's members. That included spray-painting an image of male genitals on a historic draw-bridge in St Petersburg. And that was something at the less extreme end of their repertoire.
The question is how much gyp Putin will get from other Asia-Pacific Rim leaders who show up in Vladivostok, the far eastern port city where Apec is being held.
Given the (real) White House described the sentences as "disproportionate" - as did Key - Barak Obama's diplomatic footwork would have been worth watching.
He would have fielded ticklish questions on whether Russia is sliding back into totalitarianism.
But the American president has been detained by a more pressing engagement - reconfirmation as the Democrats' presidential candidate at the party's national convention in Charlotte, North Carolina, which ends the day before Apec gets under way.
The White House has been at pains to dismiss suggestions this is a snub to Putin. However, it followed Putin pulling out of going to a G8 summit meeting in Washington.
One factor likely to limit criticism of Putin is that Apec members are designated to be "economies" rather than countries, thus enabling the participants to duck tricky political matters if they so choose.
Moreover, it is not the done thing to lecture one's counterparts on their domestic politics unless things are particularly awful. And it is even more impolite to embarrass the host.
What the Pussy Riot fiasco has done is offer the hundreds of media flying into Vladivostok some light relief from such things as "global supply chain integration" and "regulatory harmonisation" - the kind of stodgy trade-related matters which are the normal bread and butter of Apec agendas.
John Armstrong, the Herald's political correspondent, is going to Vladivostok to cover Apec.
