I was listening to some Larry Williams on the way home and it occurred to me that Brian must really be a fan, not just because he covered "Slow Down" on Another World, but Larry had a hit called "Short Fat Fanny". Sounds to me like Brian, being a fan, could have consciously and unconsciously thought of that with the lyric "Left alone with Big Fat Fanny..."
Not a groundbreaking revelation, but one of those, 'oh, interesting..." moments (for me, anyway).