All you need to do is watch it to know this is false.
I would bet money there where some fixes in Stop Making Sense.
I agree. Playing quality is way too perfect. It's really hard to dance and play the bassline perfectly timed, throughout. Presence of timing errors would "prove" it was the originally recorded sound.
It was comical with The Last Waltz. It was obvious. Danko's hands would be flailing all over the neck while what we heard was a tight bass line that didn't come close to matching his hands. That one disappointed me so much that I threw away the DVD. I need to at least "believe" I'm watching a live performance. And when it is blatantly obvious that I'm watching the equivalent of a music video, well, it ruins it for me.
If I recall correctly, Stop Making Sense was always billed as a movie about a concert, not a live concert video. They really did play, but I believe it was filmed over two nights and footage from the two performances was edited together. I would be surprised if there weren't also some edits and overdubs in the process.
The sound of the drum machine in Psycho Killer is also not really coming from the boom box and one of the backup singers is harmonizing from backstage on "Heaven."