The DM should not. IMHO. Ever.
And this is a place where our DM styles diverge.

(and you have never fudged a roll made behind the screen? NEVER? Wow... that takes some self-control.)
Not generally, because doing so can grant players information that their characters should not have.
In this case, I meant rolls like combat attacks, etc. Not rolls like search or perception that should be done behind the screen so as not to tip off the players unnecessarily.
Can you ask this question more specifically? I am not sure exactly what you are asking.
Well, I suppose a couple of things. For example, a roll done behind the screen. Have you ever fudged the roll so that it works or doesn't work in the player's favor?
Or maybe There's a plan the players concoct or a spell/ritual that they want to use. In using it or the players or PCs might be making a bad mistake or it could send them in a direction that isn't conducive to game play.
For example, a player is sitting out because his PC was captured, they are trying to find him. They use a spell or make a plan that would send them in the opposite direction, and the player would likely sit out another hour or so while the PCs bumble around. Instead, off the cuff, you place an NPC or something that nudges them in the right direction so that the player might join the game again.
these are just some (of possibly many) examples where I would modify the effects of the players' actions to move the story forward.
I think this might have to do with some of the DMing paradigm differences. I am guessing - and trying to remember from previous posts - that you are a sandbox style DM.
I don't have the time to build a sandbox campaign the way I would want to, so I run slightly modified prepublished adventures, lately APs. If the players miss the hidden door that holds the Thingy of Some Notable Importance, or their search rolls come up sucky, then I have been known to fudge a bit, and give them a bite so that they either find another clue, or search more thoroughly.
Gaming time is precious for me, so I would rather not sit through hours of backtracking, searching every corridor and room only to find that the secret compartment was in the room they searched two hours ago.