There is no cultural affiliation between current tribes and these burials and unless the bones are tested they can't show if there is a direct biological connection. So according to current law, finders-keepers....unless, using NAGPRA, which is a federal statute overriding state laws, the testing can be stopped before the decision about affiliation is made. That's exactly what happened here, but this time the "tribe" involved didn't win the case anyway.
It’s NAGPRA that requires an ancestral connection or cultural affiliation for remains to be claimed by tribes. It’s judges who have bought into tribal creation stories who have turned over remains despite NAGPRA. AFAIK, NAGPRA has not yet been amended. I think it’s fair that testing is stopped until a cultural affiliation is determined.