My perspective is different. For one thing, the native people here vary in looks. The early Europeans who arrived where I live described the people as appearing rather European in features, comparing them to Italians (except for the deep bear-fat induced tans), if I remember correctly. Across the continent the languages vary as much as they do across Europe, some say as much as they do across the Eurasian continent.
And all of these people were native Americans, not just those who appear Asian. By the time of Columbus, strains were mixed. Places like the earthworks at Chilicothe, Ohio show that trade and travel brought together people from widely separated parts of the continent. Evidence, if it's there, of some Europeans and something like Kenniwick Man show that the ancient people were a various people. Kenniwick Man was certainly native American in the truest sense--he lived here--and his genes or the genes of those like him may be spread throughout the native peoples here.
The illusion that the native people here were one people is utterly false, but that illusion is sustained by the mingling of all groups at powwows and gatherings over the past two hundred or so years and, especially on the east coast, mingling of Europeans with lingering natives, who often, tellingly, passed as European descendents themselves as they learned European customs and language.