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.

Does it really bother you that people care about their heritage? US culture is a culture that assimilates, people remember where they come from. It's almost mean-spirited that yall fault them for this. Better than forgetting. I remember where my ancestors came from because they came here from somewhere they were not wanted.

What I would ask you is why does it irk you, why do you care? Is it some hindance to my culture that I want to learn about it and try to "cosplay"? What would you prefer that we act as though we're here sui generis? Is somebody's culture lesser because they're not in that country at that time?

People of Italian ancestry in the US did not forget everything about their past, in many cultures that transition is even more recent; I remember my immigrant grandmother. Comes off as gatekeeping people who would otherwise be your relatives.

I dont know why it irks you guys. Canada does this too. It's because, unlike Europe, we haven't been here for thousands of years. My grandfather was from Dublin. He came to Canada and didn't want to go back to Ireland, ever, because he hated religion so much. But he still passed on aspects of Irish culture to us, and not because he wore green on St. Patricks day once.