That's a good question. People already memorize whole games that are notable, so I don't think it would be a stretch to memorize "the perfect game". In which case you'd basically either have to rule out people playing that game, or just not play.
You make an assumption that there is only one perfect game.
If chess is indeed a draw, many 1st White moves (maybe all) probably retains this status. And for all of those, multiple Black replies, etc etc....
Gil-Gandel: Hahaha.
That is a great story. Somehow I've never heard that one.