I know, I got that part. I'm just arguing that it is inaccurate to say that having a location be open to the public does not grant the public rights to that location. Ownership is retained by the owner no matter how many people are allowed to enter the property.
Furthermore, I'm arguing that a government owned property will be poorly managed because the owner has no incentive to preserve the resource -- why be too concerned with the state of a property you are eventually going to turn over to your political opponents? The only exception to this rule would be if the government owner was a hereditary monarch -- in which case his behavior would be much like that of a private landowner.
I'm just arguing that it is inaccurate to say that having a location be open to the public grants the public rights to that location.