In my BBC iPlayer link, Previn discusses the sketch from about 9 minutes into the programme, and about 9 mins 20 secs he says he was in tour in America and when he came back they had this sketch in mind and he "rehearsed it on the way from the airport to the BBC and we did it. It was that simple".
Which is why I said he had a busy schedule because he was on tour in America and as soon as he came back he went to the studio to do the M&W sketch. Are you saying you have proof that Previn was mistaken in his recollection of his involvement in the M&W comedy sketch?
Nope that isn't what happened, and what Previn says (note the edit half way through) is entirely consistent with the reality. This is a direct quote about the events from the show's producer John Ammonds:
'“His agent needed to know how long we would want him, as he was obviously very busy. I told them a full week. We always had the guests a full week so they could rehearse. I could almost hear a crash at the other end of the phone. Andre could not give us a full week and the best we could agree on was three days.”
“Eric was unhappy with the situation and expressed concern about how he could learn the whole routine in that time. I managed to persuade him it would be fine.”
“At the first read through I was helpless with laughter. As Andre was reading it, he was also performing it, and we all knew it was going to be great. Then trouble struck. Later that day I got a call from his agent who told me Andre had to leave. He had to fly to America because his mother was ill. Worse still, he wouldn’t be back until the night before the actual show. I was dreading breaking the news to Eric.”
“Eric seriously considered scrapping the whole routine. Based on the brief rehearsal I said it would be fine, but there were very real concerns over this. He confided in me that the routine was not as funny as thought it was. The next night when we did it for real, in front of an audience and the roof went off.”'
So the plan was that once Previn returned from tour there would be a read through of Green and Hill's long-standing sketch (which happened as planned, alluded to in Previn's clip before the edit). After that things went wrong - Previn's mother became ill and he needed to return to the USA (rather than being on tour) and the planned rehearsals therefore couldn't take place. We've no idea what Previn said in the edited section, but his comment on coming in from the airport refers to his return from his unplanned trip due to his mother's illness, not his scheduled tour, as clearly indicated in Ammonds' piece.