I think the "Brian came down and demonstrated the final part" idea is correct, from what I've read. That doesn't eliminate the possibility that Bruce did the legwork on getting the background vocals ready to lay down on tape.
Gee, it's a shame that Stephen Desper isn't here to add some interesting tidbits, YOU IDIOTS
Gee, it's a shame that Stephen Desper isn't here to add some interesting tidbits, YOU IDIOTS