"get identified", not "identify" (even if I wouldn't bet that the latter never happens, it would be a clever image projection).

A mistake on the side of the potential xenophobe that usually turns out quite positive for the misidentified. "Welfare seeker" vs "impersonation of the Marshall Plan", the difference could not be bigger. The face of the "good GI", in popular memory, has black skin because that used to be so much of a standout feature back in the day.

why would they not?

do caucasian americans identify as europeans outside of america?

or mexicans as spanisch?

African American is neither a race nor a citizenship. If you're of African descent, born in England, you may say you're African, or English, but you'll likely never say you're English African. There's a sense of heritage in African American descent but it's also very messy. A black man from England travelling to America could plausibly be called African American because it's largely been redefined as "Black but not culturally African" in what I assumed was culturally local definition.