I completely reject this analogy. In my experience, this attitude leads to exhaustion for the DM and boredom for everyone else. Players have, at the very least, responsibility for playing their characters. This gets back to my original complaint: either the DM runs everything, or the players have some agency. You cannot have both simultaneously.
Any functional RPG gives different people different roles. That's never been in question. The problem, in this case, is the DM stealthily assuming powers that should not be theirs.
I honestly don't know why this is such a sticking point. If you and I agree to use dice to adjudicate combat, and then I secretly take control of the combat results by fudging the dice, then I have both betrayed your trust and assumed powers you did not want me to have.
Is it a cardinal sin to ignore one roll, because the game is a bit broken and it would lead to an outcome everyone would find unacceptable? No. I'm not claiming that you, personally, are a bad person because you fudged the dice one time. (I do think that being open about the outcome with your players and working out a houserule would be a better option.)
However, fudging like that is a slippery slope. Are sure everyone would find the outcome unacceptable? What if you're tempted to fudge in other situations? Then you have the whole issue of WotC actively telling DMs to take charge of the game (as 'director' and 'storyteller', etc.), and offering them fudging as one way of doing that. It's extremely bad advice.