I once heard that Native Americans or American Indians actually prefer to be referred to by the name of their tribe, i.e., Sioux, Lakota, etc.
Then you've got people who have or likely have small portions of genetic heritage in obscure tribes. I'm a fifth-generation native of California, with white pioneers going back to the 1860s, but we suspect that somewhere along the line, there was an intermarriage or two with California Indians from God only knows which of a gazillion tiny and obscure tribes. Also, my great grandfather was a Sonoran Mexican with ZERO European in his blood -- he was of "La Raza," as the "hispanic" racists would say.
The whole thing is a bunch of crap and people who dispute how to define the obvious usually have a "politically correct" agenda that leans toward the left. I don't mean you personally, beejaa, but I do mean to say that getting bunched up over Politically Correct labels plays into the hands of deception and manipulation. There's nothing deceptive or maniuplative about "American Indian."