I think the separation between public and private interest may be more blurred thank you think. In an indirect ways, studios were able to spend money paying people to make those movies because the government provides a safe geographical space for that to happen. There's a reason you typically don't see many movies (certainly not entertainment movies) produced in countries ridden by war, for example. So a strong armed forces, internal police, a predictable legal system, etc., all of that is typically provided by a government and allows business, including movie studios, to run.

On a more direct way, I remember watching VHS movies as a kid in the 80s and there was an FBI piracy warning near the start of all tapes, so the studios do leverage the government to protect their business (and I don't have a problem with that in principle, if perhaps I disagree a bit with the extent of the protections).