"Ownership" just means a government grants you temporary exclusive access and they will back that privilege with law and violence, in exchange for money. It's a mafia racket outsourcing violence.
It's also ironic because native peoples typically didn't "own" land anyway. I don't know about this particular group, but most native peoples in the Americas didn't have plots that they bought and sold. So now it's only through the introduction of Western property rights that they are even able to make a "legal" claim.
Of course there is no "right" answer here, but typically throughout history when empires conquer by force, they don't later relinquish their plunder out of good will.
Gives a new meaning to "Indian giving"?