See, I come from a different camp than many of you, apparently. You play "kill the stat-monster," and I play, "show your heroism." They're very similar, but the distinctions are quite clear.
In KtSM, everything has statistics predefined, and when those statistics show that something is dead, it's dead. This is why we have things like the Challenge Rating system, so we know when our monster is suitably dangerous for the party. But of course, we all know the CR system is quite often flawed in the face of bad measurement, or merely bad rolling.
In SYH, the point of the game is not to win against the badguy; it's to be heroic in the face of overwhelming odds, ultimately (usually) winning against the badguy. A game of SYH in which the badguy is not sufficiently dangerous is a poor game, so it is the DM's
duty to leave the statistics a little ambiguous, and finagle with things in minor ways to ensure there's not a complete breakdown of the heroic action.
Now, of course, in either game, you'll get elements of the other. An SYH DM can't just make stuff up off the top of his head all the time, or else the players will stop caring how hard they try; if they can always win, then they're not as driven to come up with ridiculous ways to win. On the other hand, no one is benefited if the climax of a three hour session takes only one minute. Good craftsmanship helps make pleasing endings easier, but when things go disastrously wrong, the DM should step in and convincingly make the encounter keep going. If the players don't believe it, the DM's magic has failed. They should never know you had to add an extra 5 points of damage reduction so the villain could start to make the players think they were in over their heads. They also should never know that the reinforcements coming in from their allies was a spur of the moment decision to make sure they don't die.
You never cheat just to dick over your players, dude. You can't cheat. You're the DM. You just . . . fix your own mistakes in the middle of the game. I mean, if you'd given the villain an extra level or two when you were designing him, then things would have worked out just fine. All the players care about is having fun and being cool, so if you made a mistake when planning your session, it is, again, your
duty to set it right without ruining their fun.