That’s just bad logic saying that all Americans all are immigrants. It implies that land is bound by blood and every modern immigrant everwhere would never be integrated into society, since they weren’t the original people there. Every society that has migrated would also receive this immigrant label, like the Hungarians and Bulgarians. There comes a point where the people who conquer lands become the people living there and not just immigrants.

These kinds of bad gotchas aren’t proving anything unless you seriously think they are only going for immigrants. They are racists. They use the term immigrant to refer to non-white people.