If 0-0 is against the rules, which rule SPECIFICALLY prevents it?
Article 5 of the FIDE Rules of Chess. There it is written that a normal game (which means: both players being present at the board, and the game being started normally) can end as a win for either player, or a draw. There is no such thing as a loss, or win for both.
A loss for both players or double forfeit can only occur as a penalty for rules violation from both players, or if both players do not appear to play.
Notice here that a 0-0 could also happen if both players did not appear at the resume of a game (after a game adjournment), but today there are no game adjournments, so there is no need for a rule about this.
Some 16 years ago, there was a game in the first round of an open tournament in Greece. The player with the white pieces (a Greek FM) was winning, but he had a stroke. His opponent (an Israeli IM) tried to save him (he is a doctor) but eventually the poor man passed away. The arbiter was about to declare the IM as the winner of the game, but this kind soul claimed that he intended to resign when the opponent had the stroke, and that the point should posthumously be given to the late FM. And this is precisely what happened: The unlucky player was awarded the win after he had passed away. The IM did not play a game of chess for quite some time, and today he is a Grandmaster.
No 0-0 here either, and this is one of the most extreme cases one can think of.
Thank you. I looked at article 5 but I didn't see anything that specifically prevents a total match score of less than 1. I also looked at article 11 and didn't see it either.
I guess I'm confused because instances of total scores of less than one has occurred in competition. You said there is no such thing as a win, or loss, for both. But then you also said a score of 0-0 is possible if both players do not appear or both players violate rules.
Is it just semantics or is there a reason a score of 0-0 isn't considered a loss for both players? Is it just that the score of 0-0 isn't considered a loss because it can only happen if they don't play? Someone, it might have been you, mentioned a game between grandmasters where they decided in advance to draw after only a few moves. So both were awarded (or penalized) a forfeit. If I'm not mistaken, they were both given a score of either -1 or negative half. Either way the total score would be less than 1.

Wow. That's such a sad but incredible story at the same time. One question though (even less likely to happen): what if the other one (the IM) lost on time? I am pretty sure you have to claim the victory if someone has no time left right ? Here would it be a draw ?
This is obviously a case of "medical emergency" and it's the duty of the arbiter to stop the clock.
And when going to stop the clock, he would obviously notice if one of the flags has fallen.