In a way, the BrE is more consistent than AmE. AmE has the police are and people are, and it's not so unusual to hear the singular or plural verb form after family. When talking about the family as a group of individuals, AmE tends to use the plural verb form; when thinking of the family as a whole unit, AmE uses the singular verb form.I'm afraid, I don't see Richard's point about police and people. Perhaps he is confusing irregular plurals with singular collective nouns? Either way, it's not just AmE; You would never find the police is or the people is in BrE either, where police and people are the subject.
And is family as group versus a number of individuals really an AmE issue? In the British National Corpus, the string family + (3rd person singular verb) is over 1.5 times more common than the string family + (plain form verb). Not all of these are relevant, of course. They include sentences in which family is not the subject (e.g., The problems with the family are numerous & The nice thing about this family is...). Still, this distinction is clearly available to speakers of English on both sides of the Atlantic and there's no evidence in Firsten's column that BrE is more consistent than AmE (though it may be).