"screaming profanities in the cathedral" - this is 
  factually incorrect, they did not.

BBC thinks otherwise, reporting on "Their brief, obscenity-laced performance" http://www.bbc.co.uk/news/world-europe-19297373

Listen, I am actually against hate speech laws everywhere, including Europe, and I believe the church has no place in the modern state.

But I fail to see any Putin connection in Pussy Riot arrest and their jail time. Pussy Riot got jailed for hate speech. That's a fact. Any Putin association is a result of a well executed PR campaign. Everybody knows that... ))