I don't think / didn't say it was a problem.
Then the comment, paraphrasing, "they think they're Chinese when they're not Chinese nationals at all". If their ancestors were from China, they don't "think" they're ethnic Chinese, they are ethnic Chinese. Unless you get into the nitty gritty clans and groups of the gigantic landmass. The use of "think ... although" indicates you disagree with how they identify their ethnicity. Thus I assumed you felt it was a problem.
Apologies if I read intentions that weren't there.
Just as an example of something with a flimsier premise. Say a German American who doesn't speak the language, don't have known family there, have no loyalty to Germany, celebrate none of the German festivals, and the only indication left is a last name Schmidt. We don't say, "huh the German diaspora is everywhere" when these people say their ancestors are from Germany.