I dunno, I went to a high school reunion last year, and a dude seemed to know people's phone numbers from 30 years ago.
If he could remember that sort of thing, I can believe there are people who can remember steps of a proof, which is a much less random thing that you can feel your way around, given a few queues from memory.
Plus, realistically, how closely does an examiner read a proof? They have a stack of dozens of almost the same thing, I bet they get pretty tired of it and use a heuristic.
I think many people who grew up before cell phones remember phone numbers from the past. I just thought about it and can list the phone numbers of 3 houses that were on my childhood street in the early 2000s + another 5 that were friends in the area. I remember at least a handful of cell phone numbers from the mid to late 2000s as friends started to get those; some of them are still current. On the other hand, I don't know the number of anyone I've met in the last 15 years besides my wife, and haven't tried to.
If he could remember that sort of thing, I can believe there are people who can remember steps of a proof, which is a much less random thing that you can feel your way around, given a few queues from memory.
Plus, realistically, how closely does an examiner read a proof? They have a stack of dozens of almost the same thing, I bet they get pretty tired of it and use a heuristic.