Even the "native" peoples are immigrants. Who, by the way, may have genocidally eliminated an earlier ur-population of Eurasian immigrants who would have resembled not so much the NE Asians and Eskimos and Amerindians, but rather the Ainu of Hokkaido and other ancient genotypes found around the margins of modern Asian societies.
Exactly. This is a good point that I did not make in my first post. I tell liberals whenever this topic comes up that they're immigrants, too, not "Native Americans". They just got here 10,000 or 20,000 years before we did, depending on whose theory you believe.