Fudging dice rolls is an issue that many old schoolers particularly take offense at. They tend to be all about "the purity of the dice" and "why bother rolling at all then?" Though I would not say I have never fudged a roll, I can't think of a time in recent years I did, though I can think of a few I wish I had in retrospect.
In my last long time group, as opposed to previous long running groups made up of people I already knew who were often not that versed in RPG's, I had at least a couple of power gaming or min maxing players come along who tended to take advantage of my general good nature as a player friendly DM. As soon as they saw I had sympathy for players characters and that I almost always gave their situations the benefit of a doubt, if not a special save to give at least a small chance at avoiding perma-death, they took on the personas of jackals who sensed a wounded lamb (player character friendly DM). Yeah, give some an inch and they'll take a mile.
These are often mooks who don't really care about anybody else's fun, especially the beleaguered DM. They just wanted strong players characters who were more powerful than anybody else. For whatever reason this is the fun they got out of the game. For whatever lacked in their real lives, power or whatever (now that I think of it the wives of these dudes seemed to call the shots in their lives), they had to be bullies in an elf game. But it wasn't just for the reasonable, "fun for all" players that I was a friendly GM. Whatever the case, I was fair to all. But yeah, a few times I wished I wasn't.
But OK, I'm not here to complain about former players I often wished I had dice-fudged to death. But on the issue of DM fudging, I think there is often a deeper issue at large here. Maybe more insidious, and it's something I've noticed since I was a kid in other people's game.
You see, since I was a teen GM back in the day, I had a tendency to randomize the world in general. Most often in the case of NPC decisions. I called it my "yes no maybe" method. Kayhla the Hobbit speaks to an innkeeper and asks if they can get a free meal along with their room for the night because the party is low on funds. I think most DM's would just say yes or no depending on how they personally felt in that moment. But for me I would put that to a roll. If I had actually imagined a certain personality for this innkeeper, I would make a modifier. Is he cheap? Or is he generous? What is Kayhla's charisma? Then modify the roll. Easy enough. Well, OK, I'm sure plenty of DM's just did btb reaction rolls. But really, the rare times I sat as a player I pretty much never saw such rolls. OK, that's a fairly petty example, but you can apply that to much more.
Many DM's in my experience, my entire life, just seem to run much of the game out of their head. Mostly in terms of NPC decisions. Players pose something to an NPC, and the DM just yeah or nay's it. He decides from whole cloth what the NPC will do, how they will react. Pretty much based on his own biases. Sure, he or she might have a personality in mind for the NPC that can sway that decision. But it is still a DM decision. No die roll. It comes out of his conscious or subconscious. Out of his head. An example of one of the times I did this was as a teen. One of my players girlfriends wanted to try and play, and long story short the characters had to go to the cities fireworks factory (every game city should have a fireworks factory, in whatever genre) and get some fireworks. They are very expensive, and money was an issue. The new player had her character, a good looking woman, try to flirt a major discount from the guy. Since he was quite old (and I was quite young) I just hand waved that the guy had no libido and would not be interested. OK, again, I was young. The guy may not have still had an active sex drive, but he still might be swayed by a flirtatious young lady. I really should have put it to a roll. But no, I just decided out of my head how he would act. Long story short, the gal player was very miffed, kind of embarrassed at the failure, and quit the game right there. Sure, she could have been a little more understanding and not have overreacted so much. But it stuck with me. I gipped her, and my session, out of a cute little interaction. And that has stuck with me, and one of the reason's I believe in at least a chance of something happening.
It is probably a minor issue for most. To be honest any player I have had that I told I like to randomize even minor things in my setting for the sake of getting close to a living breathing world that doesn't entirely come out of my brain, they never seem to care much. But I think that outside of the rare times there is a 100% chance an NPC would or would not do something (somebody very against sexual assault will almost for sure not commit it. Somebody who is anti-violence will almost for sure not punch a child who tried to pickpocket them) there should be some chance at variances. Almost nothing should be an absolute. One of the things I love about the concept of The Matrix, is that the simulated world has to seem real; it has verisimilitude outside of some of the crazy powers the strongest individuals (or programs) have. If you get in street fight and you are one of the "unenlightened" then basic rules of physics are happening. What is going on is actually just a bunch of computer code dictating everything. But that code is aimed at giving a sense of a living world. I really like to think of a game world in those terms. And randomization is one of the big factors of that IMHO.
Fighting and other action pieces are in large part dictated by random rolls. Chances are modified by various factors (strength, skill, dexterity, weapon, etc). Why should the non-action stuff not be dictated by randomness to some degree or another? If not, then IMO its very similar to fudging those action dice.