Maybe I'm too attached to my love of science and fascination with genetics, but I don't understand how genetic evidence that your tribe's ancestors came from, say, Northeast Asia circa 20,000 BCE instead of having been born in the Grand Canyon circa many moons ago when the world was young would effect much of anything. Of course, as is also mentioned in the article, I'm also not worried about losing my healthcare, based on my ancestors being Siberian instead of Native American, and I am very much a member of the dominant imperialist majority. Hooray for being a white male!
A quote cited in the Genographic Project's Wikipedia article that led me to the New York Times story link, and completely baffles me, is from the chairman of the Massachusetts Commission on Indian Affairs, who's also a member of the Mashpee Wampanoag: "What the scientists are trying to prove is that we’re the same as the Pilgrims except we came over several thousand years before. Why should we give them that openly?”
Isn't that consistent with current mainstream thought? Of course, I have my doubts that this man is a Ph.D in biology or anthropology, or has any formal biology or anthropology training (how many Ph.Ds in genetics or anthropology are there in Congress? How many highly educated people who aren't doctors or lawyers routinely participate in government? I rest my admittedly fragile case), but I fail to see how this is a problem.
On the other hand, the "traditional beliefs" of my known ancestors have been various forms of Christianity- possible Indian ancestry aside, as far as I know my Welsh, English, German, and Irish ancestors would have been at least nominally Christian since probably at least the 9th century, and before the conversion of Germany, Britain, and Ireland we start delving into the tradtional Germanic and Celtic paganism that was supplanted by Christianity (which is to say, Catholicism). As a (closeted) atheist and (non-closet) skeptic, traditional beliefs don't hold much sway with me as a means of argument. I'm pretty sure that "traditional beliefs" would be cited by some Southern Baptist (or, really, any conservative evangelical Christian) who wants to counter the Infernal influence of secularism, ivory tower egghead liberals, and/or the Democratic Party, but I digress.
In short, I know nothing about the experiences of living as an oppressed minority who, until very recently, were considered to be uncivilized and therefore subhuman, and I fail to see how traditional beliefs, various benefits, and a claim to being sovereign over some land is or might be threatened by being descended from Siberians who crossed the Bering Land Bridge during the last Ice Age, and whose ancestors came from, say, Africa, rather than being descended from (for example, since I know very little about Native American mythology) the Great Spirit giving Raccoon the idea to shape the first men and women out of mud on the banks of the Arkansas River near what we now call the Grand Canyon.