A good analogy is the police suing the postal service because somone sent some illegal drugs via the mail.
Copyright organisations will lean on ANYONE to get money, they are the mafia of the electronic age in a way. They realised a while ago that suing individuals (including grandmothers, children, disabled people) was a bad PR move so moved onto the ISPs.
What they need to do to stop piracy majorly impacting their bottom line is to provide the content online at a reasonable price. iTunes makes it easy to buy TV shows but they DRM the crap out of them which annoys many people. Take the DRM off, make the TV shows reasonable priced and watch the money roll in. It's that simple. Attacking illegal downloaders won't help their cause in the long run.