I replace "American" with "U.S." because America is the Americas (North, Central and South), North American with U.S. and Canadian if it doesn't include Mexico, Latin American with "Hispanic American" if it doesn't include Brazil, Guyana, Suriname and French Guiana, and I put Iberoamerican if includes Brazil, British with UK if it includes Northern Ireland, and Middle Eastern with Arabic World if it doesn't include Iran, Israel, and Iran. Those are the proper demonyms for me to use to fill out censors in this wiki.
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What you describe may be correct from an idealized sense, but that's not common English usage at present. For example, Wikipedia just uses "American" for U.S. movies in this well-moderated example:
Also, regarding the UK, Northern Ireland is understood as a British territory, but incorporating its adjective into subjects not necessarily about Northern Ireland is pedantic. Another example here: