I think it is a terrible definition of race. It makes no sense. Your definition of country of origin is better [well, the one you found].
Of course for genealogical purposes, ethnicity as "where we were born" and ethnicity via DNA also seems to be somewhat different.
But then I was alway told when I was small that I was perhaps about 1/8 Italian. It turns out that myth started in the 1800's when someone wrote a genealogy book about that Family and SURMISED that the MIGHT have come from this Italian family back in the 1400's or 1500's just because the names were similar.