So, this argument is a natural progression from the "we were here first" argument put forth by Native Americans. Logically, since they were here first, the land was "stolen" from them. But as an extension of this logic, the Moon belongs to the U.S. on the same basis. The United States owns the moon. So there.
All that being said, I think it's rather ridiculous to assume that because the native peoples were displaced by the Europeans in North America, that it was the first time such a thing has ever happened on this planet. People have been pushed out, conquered, assimilated, and replaced throughout the history of humankind. To the victor go the spoils, as the saying goes, and it's been that way as long as life has existed.