You ever heard of a concept called "the expectation of privacy"? It's a legal umbrella for how surveillance cameras are put up. So while you have an expectation of privacy in a public restroom, you don't in the pubic building that said restroom is in. It's also why traffic cams are not usually put into residential neighbourhoods, as your house does have an expectation of privacy. And since that's a beach in a state park. I'd say that's a public space.