IQ tests do not measure acquired knowledge, so remembering facts cannot help you. Neither Fischer nor anyone who knew him ever said he was eidetic. He did have have great visual memory, a trait many other top players have displayed.
Are they all entirely different though? Assuming Fischer did have an eidetic memory, wouldn’t his memory vastly improve his score if he were to take it a second time?
Fischer's memory for his chess games was remarkable. Carlsen says he has memorized 10,000 chess games. Morphy was once asked about a game he had played more than 15 years earlier, and noticed that the printed record had an error that explained why the questioner couldn't figure out how Morphy won. This visual memory of chess games and positions is what separates the world-class players from the patzers, not IQ.
Had Fischer been an actual eidetic he would also have remembered what he had for lunch that day, what color the rugs were in the game room, what the tie the arbiter was wearing was like, and a thousand other details he never claimed to recall.
Fischer's memory might have helped if he took the exact same IQ test but not if the problems differed.
They also have had people wondering if they have photographic memory.
While yes, it is their memory that separates them from the patzers, it would lead one to believe their IQ would be better than average.
I think Brady mentioned something like this, and on better authority than his claims about Fischer's IQ. That's likely where Bill Wall got it. Problem with Wall is that he often has no idea where he picked something up. His fails to discern the quality of his source materials and simply passes on everything he reads.
He got very testy when I asked about his sources in some chess in advertising materials he posted here a couple of years ago. In that case, his sources were quite good. But, he objected to the question because the idea of sourcing historical claims is somewhat alien to his way of thinking.
Based on what others are saying, that it is possible for someone to have that great a memory, it’s not impossible for Fischer to have had it too.
There is no question that Fischer had a great memory. Wall’s story (certainly told by another) has the ring of truth. The details may or may not be accurate, but they are not inconceivable.
However, my point was about sources: do not believe what you read on Quora unless you can verify it. Do not believe something you read on Bill Wall’s website unless you can verify it. Frank Brady’s two biographies of Bobby Fischer are good reading, well-written, and some assertions are well-sourced, but not all.
John Donaldson, Bobby Fischer and His World is much different. Donaldson is clear on where he gets every snippet of information. In fact, much of the book consists of long quotations from original material (primary sources) that he has vetted. Donaldson’s work is good history.