> If one was trying to indicate that George was, in fact, a policeman, then the grammatically correct thing to do would be to add a comma after 'policeman' because it is a parenthetical phrase (i.e. a nonessential bit of detail/information).

Perhaps it's grammatically correct, but now it's ambiguous. Since "a policeman" could be a parenthetical phrase or just another item in a list. I'd rather something be obviously wrong then unobviously ambiguous.

(I'm not advocating for or against the Oxford Comma in the general case. But here, the right approach is a rephrasing, as suggested by the GP.)