You can't just define an arbitrary access list in your head and call something private. It is or isn't.
Wrong.
You can have public access but still limit that access in any way you want (unless you are some sort of entity which is required to conform to equal opportunity laws.) Next time you go get your pork skins at walmart, take a look by the door, and you'll see a sign that says something like "no firearms allowed on premises". They can do that. If you're caught violating that private policy, you can be arrested for trespassing.
Same thing at disney world.