This is one of those things that people are always going to feel strongly about, because it's easy to see how making ad hoc changes can be used and misused. For example, a misuse:
I once had a DM who rolled behind his screen all the time. This was pretty standard, so I never gave it much thought. We got hit often by enemies, but for the longest time I never gave that much thought either.
Until that one time. We were on a ship and it was attacked by pirates, who boarded us (because any time adventurers get on a ship, it's either a storm, pirates, or sea monsters, naturally).
The pirates were doing a lot of damage to us, and no one got missed the entire fight. Even when my Fighter used his Combat Expertise (reasoning the pirates weren't armored, so did I really need that attack bonus?). But I still kept getting hit. I quickly clued into what AC the bad guys had, and knew what number I needed to hit on. So I was surprised when I missed a pirate who seemed no different than the others.
"Well, maybe he has a ring of protection or something", I thought, and carried on.
After the fight, one of the other players griped about the pirates, saying the encounter was too hard. The DM let drop that they were only level 2 Warriors.
That's when my brain looked at their gear. No armor. Bastard swords, of all things. Nothing masterwork.
BAB +2. Weapon Focus for +1. At the high point of the fight, I had boosted my AC to something like 26 (the DM was salty about me wearing my armor on a ship, but I had specifically bought a crystal of aquatic action to affix to my armor before we ever got on board the ship). For them to hit me on anything other than a natural 20, they would have needed a Strength of 18. Odd for an entire pirate crew to be that strong...but then I remembered our Cleric had cast prayer, imposing a -1 to all their attack rolls. So now they would had to have 20 Strength, and since they were all human (supposedly), that seemed very unusual.
They had no magical items, nor were they buffed by a caster. And, despite the fact that the best AC they could likely have was 14 (18 Dexterity), I'd missed a few times when there was no way I could have.
So I started asking questions. The DM tried to deflect with his notes, but it came out that the pirates all had 15 Strength, to let them use their swords.
I realized that the DM had never cared what our numbers were. We could have been walking into combat buck naked for all it mattered. He wanted to challenge us, and he wasn't going to let little things like Armor Class stop him. He decided when we got hit (often), when we missed (occasionally), and when we failed or succeeded on checks, not by any rule or number, but by what he "felt" was correct.
I quit his game because, despite the fact he told a good story, I no longer had any trust that we were playing a game at all. Instead it was a sort of interactive choose your own adventure where everything was determined by the DM's whim. If his monsters couldn't hurt us, then they could. It was that simple.
Ever since, I roll all my dice in the open, and choose to be as transparent as possible with my players when it comes to the abilities of the things they fight, because keeping the trust of my players is super important to me.
I'm not saying that if you fudge, you'll lose your players. Or that anyone here abuses the tool. But it's like a magic trick. Once you see how it's done, it's no longer special. Once you know for certain it's all smoke and mirrors, you can no longer see it as a game.
And that's alright for some people. It's like pro wrestling. We all know it's fake. But for some, the storylines and the art devoted to making something fake look spectacular, are enough to keep them engaged.
And for others, it's just a bunch of sweaty, overaged men with big muscles and weird costumes missing each other by a country mile with heavily telegraphed punches.
So no matter how skilled you are at using the technique, or how much your players enjoy your campaign, people who have been burned by the abuse of fudging will never acknowledge it's legitimacy as a tool.
When hard core raiders in an MMO struggle to make their way to the final boss, and the developers are in the game, making adjustments to the boss as it's being fought, it no doubt leaves a sour taste in their mouths, even if the end result is a challenging fight and not simply beating on a pinata until it breaks open to dispense loot.
