So's your house.
Most houses are hardly considered "public property." So even a rented home is still private property.
Okay, how much "undercover" film footage have you seen emerge on some investigative news program that involves shooting of film either disallowed by the proprieters (or would be if they knew it was being shot)? (And I'm not talking about anything that would be deemed as legally obscene or exploitive)
How many arrests has that resulted in?
If somebody videotapes something and profits from it in some unlawful way, we have civil courts for that. We don't tie up our police forces and sherriff's departments who launch anti-videocam campaigns.