Nor were they "Americans" because "America" didn't exist until maybe a few hundred years ago.

Well, then, you're not human because the word didn't exist when humans came about. :) Then what can we call anyone? It's custom, and as you are an Earthling, we shove customs in front of your pompous ass all the time.

BTW, you are waay behind the times if you think they all walked over a Beringia land Bridge. There were most likely waves and the first ones likely followed the kelp down the ocean side of Alaska long before the land bridge opened up. People made it into Alaska and then stayed there long enough they have a different DNA sequence. They may have been blocked in. Also, it looks like Polynesians* made it. Another BTW, it looks like we populated the Americas, and then pushed back up into the Alaskan area and absorbed whatever population was left. Some archeologists think no one ever walked the land bridge into the Americas.

And anyone who has been somewhere for a thousand years qualifies as a native, capiche?

*Oh, looky here, I'm calling 'em Polynesians, and the concept of Polynesians didn't come about when they initially spread out from Taiwan, but if we follow that back, what do we all call each other? Different flavors of Afrikaners? There are Native American Afrikaners then, and Polynesian Afrikaners. Then, following our normal customs, we drop the Afrikaner because everyone knows it and we're back to Native Americans and Polynesians.