I hope Mr Jackson will go into detail about the condition of the source material and their restoration process at some point.
It was shot on 16mm, but was then "printed" to 35mm for the theatrical release. The film that a theater receives from the studio is referred to as a "print". The film that they used for the shoot was a negative film so it had to be "printed" onto another special type of film to make it a positive suitable for editing and viewing. If they took the original 16mm negatives, printed them to 35mm and did all of the editing for the Let It Be movie on those first generation "prints", then the original negatives, if they were stored properly, should be in excellent condition today. I believe Jackson worked from those original negatives.
For context, the show the Walking Dead was shot in 16mm and it looks great in full HD. Tons of TV and theatrical movies have been shot on 16mm.