I've seen several blog posts on this particular story. The Obama administration has changed some of the NAGPRA regulations and will allow tribes to claim remains that were found near their current or historical homelands, even if they cannot prove affiliation.
I'm going to go out on an archaeological limb here and say three little words: I don't care.
No, honestly. I predict a lot of attempts to portray this issue as an "us vs. them" fight between scientists and Native Americans, but personally I have no problem with tribes claiming remains that they cannot prove were their ancestors. Among other reasons, I'm not convinced most of these remains have as much scientific potential as some archaeologists claim. Admittedly, my research focus is not bioarchaeology, but I work in a related field. I recognize that there are new analytical techniques that have not been applied to all of the skeletons in repositories today - DNA analysis, for example - but many of these skeletons have been sitting in these museums for decades or even centuries; we've had long enough, how much more time do we need?
Furthermore, we - or our academic ancestors - have made our bed, and now we have to sleep in it. Look, none of us (hopefully) have dug up graves in a disrespectful manner, without permission of the descendants. None of us have ever owned slaves, either. But it remains the fact that we live within a system that privileges certain groups over others, and the vast collections of skeletons found in museums are the result of that bias, just as surely as the continuing differences in average wealth between communities of different ethnic backgrounds. We can say that we shouldn't be punished for the misdeeds of people in the past - today we're so much more enlightened after all - but we continue to benefit from the systematic privileging of mostly Euro-American scientists over Native Americans. It's not enough to change the rules of the game to give each player an equal chance to win, if past rounds have already given the vast majority of the cards to one person.
I spent a year doing NAGPRA compliance checks at various universities, and I have to admit that I was rather appalled by the excavations that took place as recently as the 1960's. I remember one dam project that flooded a valley with a cemetery dating to the early 1900's. The graves of Euro-Americans were moved to a hillside overlooking the valley. The graves of Native Americans were excavated by the archaeologists and the bones stored in boxes in some university's basement. Honestly, these were graves of people who had died only 30-60 years earlier. There were headstones saying that this was somebody's Uncle Fred, for Christ's sake! The mentality is mind boggling that gives a whole community the status of "research subjects", while treating their contemporaries of a different ethnicity as real people, worthy of respect after death. The people in those boxes weren't my ancestors, but the whole experience disgusted me so much that I'd be happy to return all of the skeletal remains in the country to any tribe that wanted them, no strings attached.
I will now get off my soap box.