Once every blue moon, I’ll have a player randomly want something between adventures really badly, like some specific magic item. As long as such a request wouldn’t interfere with the plot, and everyone else was cool with it, (and the player can explain in-game how they came to suddenly possess this item, etc...) I would sometimes go ahead and grant this request to keep the game moving. After all, combat was never a major part of my campaigns anyway, and we’re all there to have fun.
In contrast to this seemingly lax style of GMing, I have flat-out told other players that they would be better off looking for another group to play with, when I caught them trying to cheat or alter the game in some way behind my back.
I’m not sure what the difference is, really, but one case seems like “just having a good time” and the other seems like “dishonest treachery.” Perhaps this distinction is unfair, but it’s there in my mind nonetheless.
I banned rolling in secret from all my games back in AD&D2E- Any roll that eveyone else can't see is an automatic failure. This solves the potential problem of players lying about die results. Not that I would expect any of them would, but at least the temptation to do so isn't there.
In any case, ever since True20 became our primary gaming system, I don’t think anyone has made any such “fudging” requests at all. I’m not really sure why- Perhaps because, as someone else mentioned, True20 already has a “built-in-cheat-feature” the players can use to alter things in their favor.