Sounds like what the situation was was that they had a limited amount of time to record, and since Dean's guitar was a twelve string (and harder to retune than a six string) they didn't have time to retune it AND replay the song, so the just played the song out of tune and didn't realize how bad it sounded until after filming.
Of course, the smart thing to do would have been to pick up his 6 string Yamaha he used on Big Empty and play Sin on that while the 12 string was being retuned. But maybe they were too nervous to think of that.
Another possibility; Dean made recent comments that imply that he thought the show was being broadcast live (it wasn't). So maybe they just honestly didn't know they could take another swing at it... or maybe the schedule really did only let them play each song once.
Perhaps whoever he spoke to lied, as it seems unlikely they would forget playing a horribly out of tune version of Sin that ended up being scrubbed.
Doubt they lied about it. It's not their band, it's not their song, and it's a one off show they played a quarter century ago. It is entirely possible they completely forgot they played it since they never saw a recording of it afterward.
