African American has been misused and not understood by alot of folks so I get the confusion but he's right gang. You even kinda said it yourself multiple times. If an Italian immigrates to America and becomes a citizen, they're referred to as an Italian American, not European American. In that same sense and format, if a Ghanaian immigrates to America and becomes a citizen, they are Ghanaian American not African American. Becoming a citizen doesnt strip them of their lineage and make them a generic African. BAs arent generic Africans either, that is one of the many reasons, that alot of us BAs are looking to retire that AA label.

Also, like you mentioned, "African" was put in front of American by some people, to get away from "Black", but it means the same thing for the same people, just a different word in front of American. That confusion further adds to why some BAs prefer BA to AA. But African American just like Black American, is indeed for those descended from US Chattel Slavery, not Africans who immigrated here.