In short? Authenticity. If one surmises (as some folklore researchers do) that aliens represent a secularized version of angels and demons, then Natives provide a link between the extraterrestrial (with their almost magical superior technology, not to mention being from realms unknown) and the terrestrial. If aliens have been around since the so-called ancient times, then only those peoples with ancient memories can attest to their reality with any surety. And Natives are perceived to have maintained an unbroken link to their ancestral heritage, including being able to translate petroglyphs that seem to show people meeting with alien beings.
With regard to the endtimes, the nature of the apocalypse in North America has also become increasingly secularized. Though there are still plenty of people who stick to Judgment Day according to the Book of Revelation, many people consider a more nature-alized scenario, where natural (or, again, extraterrestrial) disaster will wipe out great swaths of humanity.
Once again, with the general "expectation" that Natives have a stronger connection to the natural world than anyone else, a prophecy that predicts any major world change (often turned into an end of days scenario) provides authenticity. It absolutely does not matter whether such prophecies are "true" or "false," "real" or "not real." What matters is the affective relationship non-Natives have with their expectations of Natives in order to provide validity to apocalyptic scenarios or to visitations by alien beings.
(sorry for the book....had to get it out while I was still thinking about it.)