I don't understand what "open to the public" means. I suspect that a complaint on those grounds is grasping at straws from a coalition of NIMBY neighbors and entitled hikers.

If I buy a property that people have been illegally trespassing on for years and put a house on it, is that open to the public?

I would think you would have to explicitly post permission to be on private land because I assume it's implicitly not permissible to trespass...