While I don't support the incarceration of Pussy Riot, can you imagine what would happen if Anal Cunt barged into a service at, for example, St. Paul's Cathedral in London, and started singing and swearing and blaspheming? Don't forget, the Sex Pistols were arrested for performing God Save The Queen. One of the women who was convicted also took part in an orgy in a museum, and is part of a group that (amongst other illegal acts of shock-protest) shoplifted a raw chicken by inserting it into a woman's vagina.
I think three years is extremely harsh, but to dismiss the charges as "chanting an anti-Putin slogan" is massively oversimplifying the issue. Were it to have happened in the UK, I would not be surprised if there were a (short) custodial sentence.
I don't disagree with your main point though, corruption is rife, and despite attempts to rid the country of it, it almost certainly goes right the way to the top. Russian people have next to no faith in their legal system.