This issue doesn't neatly divide one faith against another. Some Judeo-Christian creationists have little interest in the fossil record or whether tribes prevent us fom knowing more. (I don't personally know any creationists who think this way, and I'm something of one myself.) And politically, contributions from Indian gaming groups is a bi-partisan affair, often benefiting whoever was lucky enough to be in office when the casino bill passed.
When it does, members of nearly extinct tribes come out of the woodwork, and everyone starts sifting through their genealogy hoping to prove the same. I know, sometimes the gaming revenue doesn't disperse as well as it should, but something is better than nothing. The right to profit this way - and the right to prevent others from doing the same - is one of the big perks believed to be at risk when non-Indian fossils come out of the ground.
Still, there are other reasons to avoid changing the current benefits system... Wounded Knee and all that. So why destroy bones? It changes very little in the long run. This cover-up might even hurt Indian relations with the voters someday. Practically everywhere else in the world, human remains this old are no longer sacred.