I seem to remember reading somewhere that John asked if Paul would contribute his bit to the song. (Paul was working on that bit he sang in A DAy In The Life for a song of his own). Paul agreed and the bit got added in.
Personally, I think it created a great transition between segments of the song and was perfect for it.
Not living in England I can't comment on the BBC, but they seemed to want to ban just about everything that seemed even remotely controversial. Perhaps we should ban the BBC?