I think the person who first used the phrase is using an imprecise rhetorical flourish.
Nevertheless, Mitochondrial DNA markers can be used to determine everyones ancestory. Therefore, the amalgamated group I mentioned before will show a common thread of ancestory from the relatively small number of pre-1880 (and even more so pre-1800) immigrants to this country.
BFD! Not a single one of my ancestors set foot on North American soil before 1905--most of them came over in the 1920s. Guess I'm not an American, right?
Being an American--claiming to have allegiance to ANY nation, for that matter--has nothing to do with genetics. Nada, zip, zilch, zero. Ideals, baby. I am an American because I would fight for my country and I would die for my country. Being born here just means I can run for President.