Noctem
Explorer
I think the real issue is that players and DM can not read each others minds, so "enhance the story" is an inherently subjective thing - meaning that for a particular instance of fudging, only what the DM subjectively thinks of as an enhancement is taken into account and player opinion might differ (unless, of course, the DM actually asks the players for input before changing something - but that's not the kind of fudging that anyone's been talking about thus far).
And when it comes to "move the story along" fudging, most of that comes down to situations like the DM coming up with what they thought would be a particular sort of challenge and they were incorrect because they didn't account for character ability or the choices that a player might make, and I have a personal opinion that to fudge in those situations doesn't actually help the DM better their DMing, while actually admitting the mistake to the players and working together to move past it does.
This is pretty my stance on it as well. Fudging by its very nature is about the DM deciding something which will influence everyone else at the table in secret. That's why I called it a selfish act in the other thread. You're doing what YOU think is the best thing for everyone, without asking for consent or input, in secret. I've admitted many times that I've made a mistake in play while DM'ing. Mistakes WILL happen. Fudging though as a result of a mistake doesn't seem, at least to me, to be the way to become better at DM'ing.