When the rules are not useful, they should not be used. This is not the same as saying that they should be broken. This is saying that they should be invoked when they are needed, and set aside when they are not. The simple example, which I'm pretty sure everyone here generally agrees with, is when a player proposes a course of action which simply should succeed (or should simply fail, but I prefer to pick the positive example here). The purpose of, for example, a skill check or an attack roll, is to determine a result when we don't know what the result should be. But in those cases where we already know that an action simply should succeed, flat, no questions asked, then....the rules for checks are therefore irrelevant in that moment. There is no need to invoke the associated rules; this is not breaking them, it is respecting that the situation at hand has not actually called for their use. Likewise, if it is very obvious that the party simply cannot lose a battle anymore, but it might take a dozen rounds to resolve by slowly whittling down the remaining stragglers, openly asking, "Should we just call this fight over?" is not breaking the rules of combat, it's saying, "We know what the rules will produce. Do we need to go through all the steps, or can we skip them?"
In order for a rule to be set aside and not be breaking the rule, the rule itself needs to be worded with the ability to set it aside when the DM feels it's needed. Otherwise, it's breaking the rule.
When I talk about breaking the rule or altering it when circumstances make it inappropriate to use, it's the same thing you are talking about there. In that particular circumstance the rule as it is written is not needed and should be set aside completely, in part, or in part and altered a bit to make it fit the circumstance appropriately. This is not a change to meet some desire of mine regarding how the fiction will turn out.
From that paragraph, it sounds like we are all or mostly on the same page there.
The place where this principle is most put to the test is, in my not-so-humble opinion, when the GM strongly feels that a certain result should (or should not) happen, but the rules have already been invoked and clearly produced that outcome...but only to the GM. That is the moment when "fudging" is a temptation. "Fudging", at least as I define it, is the act of secretly (the secrecy is extremely important) breaking the rules in order to disregard result A (the one the rules indicate) in order to create result B instead (the one the GM prefers, for whatever reason), and then concealing this fact from the players so they cannot find out that the rules were not actually followed.
If any of these three elements--the secrecy, the disregarding, or the concealment--are not actually done, then the action isn't "fudging" (as I define it). So, for example, a GM looking down at the die someone rolled and realizing they shouldn't have asked for a roll at all? If they just come clean and admit this, and propose an alternative, that's not fudging--it's admitting that the rules should never have been invoked, and thus weren't appropriate to begin with. Or, if the GM swallows their dislike and lets the result stand, obviously that's not fudging. Or, if the GM does change the result, even non-openly, but makes it practically possible for the players to learn that and how it happened (not merely theoretically; the players really could find out that something changed), then it is not fudging--it is instead inserting new diegetic elements which change the situation.
My standard examples for this are "the party kills a boss-creature 'too quick' and the GM wishes for the boss-creature to last longer" and "the party has TPK'd, especially in an utterly unforeseeable or ridiculous way, and the GM wants to do something about that". The former is not a positive for the PCs (a fight they "should have" won is not over yet) while the latter is (a fight which "should have" terminated them produces a different result). IMO, there are three alternatives to fudging in these situations which still achieve all of the results of fudging (and more!) without any of the downsides thereof. They are:
You probably won't approve, but there is only one set of circumstance where I will fudge.
Very, very rarely, through no fault of its own, such as bad decision making or bad tactics, the party finds itself the victim of incredibly bad luck coupled with me having incredibly good luck. They can't roll above single digits and are missing the monster(s) and critical saves, while at the same time I'm making saves, hitting left and right, and rolling multiple criticals against them.
When that happens I will fudge a few rolls. Some hits become misses, and some crits become normal hits. I do want to stress that this is not to allow the group to win or even have an advantage. It's just to give them a fighting chance rather than TPK them over extreme luck.
As I said, those particular circumstances are very rare. The vast majority of the time the extreme bad luck and extreme good luck are not present together Those few times where they are together, often the group has made some sort of mistake as well, such as in the last campaign when the group down most of their resources and hurt, decided to attack the drow priestess and her cohort who they knew were ready for them, instead of leaving the dungeon and resting first. I held nothing back and fudged nothing. They won with only a single PC death, and they only did that well because their dice were on fire that night. It should have been a TPK, but wasn't.
My campaigns last about a year. I've never seen the extreme bad/good luck coupled with no mistakes more than once in a campaign, and usually I go for 2-3 campaigns before it happens.
Edit: Forgot to respond to this.
- Make clear within the world that something mysterious and weird has just happened: make the divergence from the rules' result diegetic. E.g., "The goblin-priestess took a lethal blow, you KNOW it was a lethal blow, she should be dead. But then she stood back up again, bleeding profusely from her sternum, eyes aglow in violet, babbling madness in Abyssal." Now it's a mystery--but, importantly, a mystery you as DM have time to build a good, well-constructed answer for.
That's something that I would never, ever do. To me making up something so that I can keep a BBEG alive longer is far more egregious than the rare instance of fudging. If the players' strategy and tactics, even good luck, have made the BBEG fight short, that's awesome for them. It should be honored and rewarded, not held back.