"And infinite games only matter if the person plays randomly thereby making all combinations possible. Humans don't play like this"
Well in some sense they do, actually. We have certain procedures we do in our heads -- for example we may check for all checks and captures, or at least tell ourself to do this. Yet we still miss checks and captures. That is pretty typically human chess, actually!
If we assume one condition is that both players are well rested, motivated, etc and trying to win, then I think you can't say they will play truly random moves.
Unplanned, sure, but not random. For example I may attack a loose piece, completely missing my opponent has mate in 1, but I was still thinking about loose pieces.
Just to respond and clarify the above post: Don't get too bogged down in theoretical minutiae. There is a deeper underlying point that you seem to be missing regarding 1300s and 2700s. These are just abstract landmarks signifying strength. Unfortunately, this is not theoretically pure because we are not clearly defining the signification. We don't even have an image of 1300 or 2700 clearly in our heads! What this discussion should actually read is: Can a super GM ever lose to a patzer? The answer would be no because, by definition, a patzer does not know how to play chess! Therefore theoretical debate is already stimied by undefined misconceptions and you two are probably arguing with different images in your heads. Regardless, another question: If a 1300 player beats a 2700 player, is that 1300 player really just a 1300? Maybe he is 1300 for now but he is on his way up, or maybe he is getting better from playing the 2700 an unspecified amount of times.
"Also, the question is not about the practicality of playing thousands of games without a loss where we start to look at outside factors like fatigue or mental stress."
Right but we can make up scenarios that don't have this problem. For example, the person gradually accumulating an amount of games, playing the 1300s (as well as whoever else he plays in tournaments) might not be taking count of those games, but if we were to take statistics of those games, we might see some games are closer than others, etc, and maybe we would find an oddball somewhere, even if it was over the course of decades.
And of course this would take a long time so we'd have to assume chess players are immortal for my example to carry out probably, etc etc., but it doesn't really matter. The point remains that small likelihoods occur in large samples.