The players still need to feel like the GM isn't out to get them, but is even rooting for them.
I don't fudge, and my players know, explicitly, that I'm rooting for them. I'm always a little apologetic when one of them dies (and it always matters in-game), but I'm not going to fudge it. I've had way too many cool things come out of deaths / setbacks for me to stop it, and I'm not about to fudge things when I know they like earning their wins.
I just had a player die fairly recently (5-6 weeks ago?), and the player was happy about it. He loved that character, and even feared that he'd lose interest in the campaign if the character died. His character was a berserker / paladin type of character (I don't play D&D, so this is the closest analog), and the city he was in had been attacked by a large force outside that had already destroyed the keep with magic. The general said that they would eventually lose the fight due to morale / inferior magic, and so my player sent his character out to duel the very powerful warrior leader (his power and prowess had been well-known for quite a while in-game). But, this guy was responsible for sacrificing a fellow knight to power his ritual to destroy the keep, and his brother (a powerful warrior) had killed this PC's squire and friend during the initial assault, and the bad guy was now getting ready to attack the town, kill everyone, and burn it down (killing tens of thousands of people).
So, he goes out and gets in a one on one duel with a much higher level character, and through good luck, lots of resources, and not backing down, he killed his enemy. However, he died a few rounds afterwards due to the wounds he had sustained from the fight, in the arms of his squire's best friend (a squire to another PC). The enemy force had been united under this warrior leader, and he was the one who knew the ritual magic, so they immediately started some minor infighting, but were organized enough to retreat. In the chaos, though, two hostage knights and a few other captured good guys escaped.
Out of game, the NPC was a level 16 warrior that could transform into a beast (and he did during the fight), and the PC warrior was only level 8. But, I didn't fudge the fight; the player (and PC) knew what he was getting into, and I'm not going to throw the fight. However, like I said, good luck and expending significant resources let him kill the bad guy before dying in his friend's arms (the best friend of the man he wanted to avenge).
I think this is a great story, and my player -while initially sad about his character's death- thinks so even more than I do. Sure, this could have happened if I fudged, but my players aren't stupid guys; we're all above average in smartitude (as many RPGers are), and they can pick up on signs of fudging. But, I rolled in the open, and I was consistent with his attacks. I even showed the player the bad guy's HP when a critical hit dropped the bad guy to 1 rather than 0 or below. But, the players know that the win was earned, and that makes my players (repeat:
my players) so much more invested in the game.
In this regards, if I fudged things when they think I'm not going to, I'll be cheating. It's not what we agreed to play, and it's not what they're expecting or what they want.
If the GM makes a roll with a result that is highly unlikely and thus derails the story, then I have no problem with that roll being ignored. Of course I don't want that to happen much - sometimes things go in unexpected directions. But there are also times when a story "feels" like it need to go a certain way.
In the games I've been running recently, I have made an effort to have a lot more group input. I think that addresses your "different strokes" issue. Sometimes it is better to be above board about the "cheating" so everyone knows you're trying to keep the game interesting for everyone. It gets tricky when you have huge power disparities. All the more reason, I think, to get the group in on the behind the scenes stuff so ou have buy-in from the start.
I agree about being above-board about it. If you do that, I don't think it's cheating, and it can certainly make the game better / great for a lot of players / groups. I have absolutely no problem with other people doing it, but, personally, I don't like GMs fudging my stuff, and I don't like doing it as the GM. It's all just preference, though. Which boils down to -as always- play what you like
