I've read & heard that very story since I was a kid being that my Maternal Grandmother is Native American, no argument in that fact, 25,000 years which can be debated give or take a few thousand adverse to 500 years which is well documented throughout history. The premise here, the native American has more of a justified claim of squatter's rights if that term may be used. So as you stated, no indigenous people exist technically, maybe with the exception of those created in the Garden of Eden.
So in the year 2104 what do you think we should do to be fair to everyone no matter when their ancestors came to the American continents? I see that as the key question that needs to be answered. Should you pay less taxes because you are 1/4 Native American? Should a black person pay less taxes because his great grandparents were brought to America as slaves?
Since life isn't fair (as is crystal clear by the horrific treatment of Native Americans at the hands of the white man) and the best we can hope for is a compromise, and since the American Indian has done nothing BUT compromise over the past 500+ years. I submit that it's time for the white man to to suck it up for a change.
Everyone's entitled to their own opinions, but not their own facts.