Long ago, the nations of the world made an agreement that none of them could claim rights over any heavenly bodies, in more than a "local" and "current" capacity.
This is the loophole that these people use, they go and register themselves as claiming the land/moon. However, when it comes time to defend those rights, none of the countries in the world will acknowledge them, and there will be conflicting individual claims over different things.
Don\'t waste your money. I can claim I own anything I want... it only means something if there are laws and countries backing that up.