Not in the least. As a matter of fact it is the EXACT opposite - as a practical matter this is EXACTLY what it is. Public ownership is the collective ownership of the land by the people of this nation and we have the RIGHT to regulate who and what we allow into the nation.In a way it is. The 'public domain' is nothing more than land that we all own. I have a right to cross it under most circumstances as I am one of the 300 million owners. Random man in China however does not - they have no rights over that land and are not one of those owners. The same can be said in reciprocation.Does your neighbor have the natural right to move into your basement? Property rights are natural rights as well.
If the above is a no, then why do we, as a collective people, not have the right to determine who comes and goes in our house - the USA?
No, neither my neighbors nor anyone else have the natural right to freely move into my basement, and the reason is that my basement my private property. Movement in and through the public domain is not at all the same thing.
Oh, come on. You know you are pushing the limits of what it means for lands to be part of the public domain, and I say that because you and I both know that the only thing making you and I "own" the U.S. public lands is a set of man made laws, not natural laws. I see your remarks above as academic, and for this discussion, they are surely intriguing for the sake of intellectual debate, but as a practical thing, which is what immigration amounts to, not so much.
Further, I could make the exact claim about all property rights - they are a set of man made laws and not natural. That argument would be incorrect IMHO but it would not differ from the one that you are making.