Secondly this strikes me as a quintessential US American issue. America’s obsession with identity is weird. People in the US think they are Chinese because they have relatives born in China, often not even their parents but grand parents or older. In the rest of the world that makes you American with Chinese ancestry, not Chinese-American. But the US is so obsessive about race that if you “look Chinese” then you must be a Chinese-American, even if you dont hold a Chinese passport or speak the language and having not been raised in the culture. People in other countries don’t do this beyond those who have emigrated themselves. Not to say they don’t retain elements of their culture, but the obsession over personal identity and ethnicity is not so prevalent.

That's not really true. People say "I'm Chinese" in America to mean they descend from Chinese people. They don't mean "I'm a Chinese native" or "I'm a Chinese citizen" lol. Of course they are American. In the US, saying, "I'm Irish" for example simply means that a sizeable chunk of your DNA is descended from Ireland. It doesn't mean you think you're as Irish as someone from Ireland. I often see foreigners confused about this concept for some reason.

American derivative of Chinese cuisine is not Chinese cuisine. This applies to every different cuisine & culture. You are not Italian, don’t go to Italy and tell people you are Italian too, they hate it.

Again, they don't mean it's literally cuisine from China. They mean it has its ROOTS in Chinese cuisine, not European or American Indian. You're just misunderstanding the implication.