Saying that an American man is British is like saying because Great Britain colonized some part of Africa it then makes people of those Africans countries colonized by Britain as British people. So to answer your question op from my own end based on knowledge Americans are not British. They are tow different people entirely.
This really answers OP question, if an Americans man is a British man, because the former colonized the latter, then me as an African man, who's country is also colonized by the British, makes me British too. We should understand that america, is a multi ethic country, so we can not call them British, because they have people who's origins are Britain. What about Americans whose origins are Chinese, will you say Americans are Chinese? What about America's native indians, can they also be called British? Maybe if a person has dual citizenship, then I believe that the person can be identified as a citizen of the original and adopted county
