cheers, BackPacker!
I agree that there seems to be an inconsistency on the flightschoolcandidates website - and given that you were made to jump through the hoops, I'd guess that you're right! In which case, I imagine that the person writing the FAQ didn't envisage students in the US studying for non-FAA qualifications, so wrote "FAA certificate" when he or she meant "any flight training certificate".
I'm thinking of going to Anglo-American in San Diego - trawling the forum, it seems that a number of people have said good things about them in the past. I'll contact them, and update the thread with pertinent facts.