Hey, first of all, I apologize for a typo in my previous response here. What I meant to type was, "I'm not sure why you think the same method could NOT have been used for his vocals in the ensemble number."
As for "The Rain in Spain," although I don't know all the details for certain, I can assure you that Marni was not standing there on the set and singing the lyrics while Hepburn lip-synced! Audrey was either lip-syncing to a pre-record of Marni's voice, or to a pre-record of her own voice (Audrey's) and Marni looped in the sung sections later. I have never been sure whether the talking, laughing, and horse play during the number was recorded live, or lip-synched, or looped, though it SEEMS to me it was NOT recorded live.
I'm glad you watched that documentary. Yes, it's fascinating. Fun fact, and I don't remember if it's in that docu, but the cinematographer for MFL was the same fellow who, years earlier, had served in that same capacity for the film of PYGMALION: Harry Stradling.