"In all of the United States, there's only about eight skeletons of this age known."
...and they all are the Kennewick Man variety. There are no 'Native American' remains (as we know then today) that are older than 6,000 years old!
That business about the Indian remains law, if anyone is interested, could be solved sensibly.
If remains date from within last 750 years, they are presumed Amerindian of continuing cultures and will be returned to the tribes BARRING some overwhelming public need.
If remains date from within last 1500 years, they are presumed to be of Amerindian race and will be returned to some tribes or other, again BARRING some overwhelming public need.
But, and this is key, if remains date to over 1500 years ago, they will be presumed to be of unknown race and origin, not connected with any current people, and subject to all scientific investigation as to what and who they might be.
BTW Even within the 1500 years, a suit could be brought contending the remains are European or Asian or African and (were it successful) the bones could escape the Native lockup.