It's not theft, though. Copyright infringement is civil, not criminal (correct me if I'm wrong). Filing a suit against someone is a more apt analogy, and nobody gets to file for free unless the lawyer thinks there's a good enough chance at a monetary award.
I think technically you are not wrong but actually depending on how angry the media corporations are you can get your assets frozen or be extradited like a criminal.
Very good point, and I wonder how the same amount of false theft reports would be handled by the police. They might tell the person filing the reports they have to stop crying wolf, or perhaps start ignoring them altogether.