Their interest is in protecting their property, which is something the government has a duty to assist them with. And contrary to what was said in this thread, private entities can't shut down websites, the Justice Department would be able to do it (subject to judicial review) or a court order would have to be obtained. As far as You Tube, that situation has been resolved, there's no chance they'd get shut down.
Read the bill again, which other organization or individual would have their property rights enforced like MPAA and RIAA? none. Which is why this bill should be pointed at, laughed at, and be burned up.
If someone steals from me, I can go to the police and they have to take action. How is this any different?