It seems, that people do not know that in USA there exists American ethnicity of relatively small population(for USA) - about 20 million that identifies themselves as Americans, so the quote is not correct.

However large majority of Americans have background of immigrants and they have right to claim their ancestry(though DNA companies are selling them as ancestry lineage their relatedness, which is not the same). You and other people that wants to gatekeep this have no right to decide for them what they want to identify as, just as Europeans nowadays are mixing up national identity and ethnic identity, which are not exact match even in Europe.