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.
It makes for good rumours and TV show plots, but this sort of "photographic memory" has never been shown to actually exist.