If your DM notes state that getting the NPC to do something requires a DC 15 Persuasion check, but then you end up not even asking for a roll because the roleplay was good enough that you just let them auto-succeed... that is also "fudging". If you do that, you are a fudger. You were not letting the dice roll where they may when your notes stated the requirement for success. You essentially fudged an automatic '20'.
And this is why I don't care about fudging. Because I'm not going to let my notes or the dice be a roadblock to good and fun play.
I don't think this sort of it's-all-relative-so-nothing-matters approach is helpful for this discussion, since now you're getting into meta territory. One of the core functions of GMing is deciding when to roll dice and when not to. Just like you don't roll for each step a character takes or to see if they die in their sleep from some undiagnosed congenital disease, no one would reasonably advocate for every single moment in every game to be determined by chance. Likewise, no adventure, no matter how painstakingly prepped, is some hyper-detailed Matrix-like simulation that PCs are interacting with, where all variables are known and accounted for. (Not that that would be any fun anyway)
What we're really talking about is what happens when the dice come out, for all the reasons they come out, nearly all of which are determined by the GM. The exact reasons for rolling can vary by system. A lot of modern indie-leaning games are very explicit about the idea that you really shouldn't roll if there's no risk involved. When I'm running something really trad, like Shadowrun, I call for tons of rolls, since I think that system models the world and narrative though rolls, including ones where there's no risk for failing, but a high degree of success could move things in unexpected directions. If I'm running PbtA I'm not asking for rapid-fire rolls--the game would fall apart.
So different games and GMs ask for rolls at different times. But the fudging we're really getting into--or maybe what I'm most interested in--is numerical tweaking once a situation has come to a roll. And while no one's really going to change anyone's minds here, I think it's interesting to see the main, specific points both sides have landed on (when folks aren't doing the forum-poster thing of flipping out about a specific word choice or dictionary definition). My interpretation and words, obviously:
Pro-fudge:
-Don't let luck get in the way of a group's good time, which is why we play games in the first place.
-Fudging can help GMs fix their own prepping mistakes, or an adventure's sloppy encounter design.
Anti-fudge:
-Fudging turns RPGs into less of a game, and more like a GM-presented play, and turns players into unwitting actors.
-That fudging is nearly always secret is proof that GMs know it's paternalistic, unsavory behavior that most players would object to.
I'm fully in the latter camp, and I find the whole fudging secrecy bit particularly damning. There are countless tools and techniques that GMs can use to shift gears midway through a session or encounter that players not only process out in the open, but are thrilled and impressed by. Maybe reinforcements show up, but now the PCs owe them. Maybe a beloved NPC sacrifices themselves to save a PC or defeat the enemy. Or the enemy just decides to leave, and maybe comes back with their own reinforcements. And only in a system as trad as D&D would any of that seem like gross fudging to a super-strict player. Games like Blades in the Dark or Dungeon World build those kinds of improvised dramatic developments into dice rolls. A DM doesn't have that mechanical support for when and how to improvise, but they're the DM--they can just make it happen (as long as you aren't playing AL, I guess).
But if a GM rolled in the open, and reached over and poked the d20 until it came up with a different face? Objectively weird and potentially table-detonating. And what's the difference between doing that in front of or behind a piece of cardstock (or the virtual equivalent)? You know that nearly every player would find it jarring and repulsive. You know this, or you wouldn't hide it. And if you fessed up to it later, it'd still be appalling behavior. Think about all the times a GM has talked, after an adventure is over, about how they expected this and prepped that and had to improvise such and such and what might have happened if the PCs had done something else, etc. Now imagine the GM also saying "Oh and I made sure that one guy missed you because I thought you'd be sad about it, but another time I made sure the big bad hit because I would have been sad that he didn't seem impressive enough."
I don't think the players would be into that, to say the least.
EDIT: I should have said "are
sometimes thrilled and impressed by," re: GMs dropping some obviously improvised narrative beat into a scene. Obviously depends on the group and the game's tone and the GM's execution in the moment.