I may have missed something, but I thought this discussion was about the DM changing his own rolls for the benefit of the story and enjoyment of all.
That is all well and good assuming the players have come to the table with the expectation of telling a story. If that is the case then there is no controversy.
Here I am going to disagree with EW (not in a way that will surprise him, I don't think).
If the players have come to the table with the expectation of having
the GM tell them a story, then GM fudging "for the benefit of the story" may be all well-and-good. This is White Wolf's "golden rule" from their 90s so-called "story teller" games.
If the players have come to the table with the expectation of
playing the game, including making their choices and using their resources,
in order to see what story results, then GM fudging is a unilateral assertion of authority that the players haven't agreed to. For instance, if the players choose to fight rather than to negotiate, or surrrender, or run away, then they have chosen to stake their PCs physical wellbeing against whatever good outcome they think will result from the fight.
That's the starting point for the story. GM fudging is unauthorised authorship.
From my perspective, if the players didn't want to stake their PCs' physical wellbeing, they shouldn't have fought. And if the GM is constantly putting forward situations where the players don't have any emotional response and so don't deliberately care about what they are staking (eg filler combats) then the GM need to write better encounters!
Not everyone plays this way. But some do, and for us - just as much as for a Gygaxian like ExploderWizard - fudging action resolution is not a useful tool.
by skipping die rolling in many cases, you're already situationally fudging the rules.
It's overt. Which is one difference, and perhaps the most important.
Some games also have a rule along the lines of "say yes or roll the dice". 5e can be played as such a game: p 58 of the Basic PDF says "The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure." Nothing stops the GM from deciding that considerations of dramatic pacing, fairness etc can be one factor in determining whether or not there is a chance of failure.