The point here is that space will not be developed without property rights. That is in the President's Commission report and that is being ignored, and not only by NASA--they cannot do anything about it, it is a legal problem--but by the President, the White House, Congress, the USSC, and by all private entrepreneurs including the ones represented in this article. None of the get it.
The Chinese can build an installation on the moon.. just as much right as us..
I would assume there may need to be some negotiation of "territorial" limits or some such diplomatic garbage, but that is all well and good.
I would think that it would be understood the Chinese or Russians, etc.. would not be expecting to "tour" our facilities any time they felt like it, unless such arrangements were totally reciprocal..
I believe there are some agreements concerning arms in space, that may or may not still be in effect that would guarantee access for verification of those treaties..
But if you're talking about our building a facility and the Chinese or Russians, etc., having some sort of "right" to move in and take up residence, I don't think that would apply..
Just as any spacecraft would be considered "sovereign" vessels of the U.S., so would our installations or facilities..
We'll never have property rights on the Moon or on any other real estate in space until some granting authority that actually respects private property rights, claims the Moon as its own and begins handing out/selling land grants to individuals and businesses. At least that's how I see it. If we wait for China or the UN to agree to the establishment of private property rights in space, it'll never happen! We have to claim the Moon as American territory.
Also possible, but much less desirable imo, is to claim a large chunk of it and let other nations that actually get there, also claim their chunk. I'm not a lawyer, of course, as you can tell, lol!