I haven't been able to find much about the legalities involved in these restrictions. How can a private company impose restrictions on public roads and beaches

I haven't been able to find much about the legalities involved in these restrictions. How can a private company impose restrictions on public roads and beaches and land they don't own? Is there a governmental agency that will actually be imposing these rules? I can imagine the FAA clearing the airspace, of course, but what about the land/water?