To clarify this, for those who have not clicked on the link about Kennewick Man, although some Native American groups wanted to rebury the remains, they lost the legal case (at least for now). The remains were not reburied and have been made available for scientific study (fortunately).
This is purest nonsense. They may have oral traditions, but they have no idea how far they actually go back. Many Native American groups have moved around a great deal, both in historical times and earlier. Showing any geographical continuity would have to depend on archeological artifacts or the genetics of skeletal remains. As far as I know, this can be done for few groups beyond a few centuries, and for none beyond a few thousand years at most.
This said, there are a few Native American legends that may date back to the post-Pleistocene. The “Thunderbird” may correspond to the now extinct giant vulture Teratornis. But if groups have oral traditions that “go back 30,000 years,” why is there no clear mention of such distinctive animals as mastodons or sabre-toothed cats?