Little known fact about the Inca was that their civilization was barely over a century old when Pizzaro arrived. They were big on the purity of the blood line so brother-sister marriage was not only common but encouraged. They were only a generation or two away from a really inbred ruling class and all the fruits thereof.
Reportedly Native American leaders have decreed that no Native Americans should take DNA tests, but I don't know how that could be enforced if someone of Indian ancestry chose to take the test. And there are many people who have some documented Indian ancestry, many of whom have probably taken the tests, so it should be possible to determine the DNA indicative of ancestry from Indians living in the US.
I have no Indian ancestry but some relatives married Cherokee women when they were still in Georgia, and accompanied their wives and children on the Trail of Tears. I have been in contact with a distant cousin who is descended from one of those Cherokee/white (Scots-Irish) marriages, who showed up as a match on one of the DNA sites.