You're right - some of the players are not hooked up to the main sound - specially bass, I think, as that would get real muddy fast.
But a lot of the drummers are in fact in synch - look at the long shots. When they do close-ups of the drummers, the editing wasn't very tight to the music.
When they do closeups of the girls singing they seem to be accurate. You can see on closeups of guys together on guitar, that some are just enjoying themselves and not really playing along.
It wasn't done to 'break records' (like this one:
http://globalnews.ca/news/1306963/new-r ... s-hey-joe/ ) but to show spirit of harmony - Shmed did you listen all the way through and listen to the speech by the guy at the end?