Well, what I would ask, though, is this: why does it matter if we're playing the game "as intended"? Seriously, why is that important?
I recently got a message from a gamer in Brazil who's playing Phoenix. He said that his group very much based their game on Heroes, the TV show, and therefore they'd adjusted a bunch of the rules around power allotment. He was kinda sorta asking if that was "okay." My response was: he/his group is having fun, they're achieving the "feel" that they wanted, the game is working for them. Whether it's okay with me or it lines up with my intentions as the designer is immaterial to the conversation at that point. I'm just delighted that he's having a good time! I mean, to me, the shining glory of RPGs is that you make your own fun. I played 2nd Ed. for 10 years and not once did anyone run a packaged module. It was all DIY. So the idea that the GM can't fudge some hit points or ignore a roll here and there seems really alien to me, just to bring it back around to the subject at hand.
It also occurred to me while I was invigilating a test this morning that calling that kind of thing "cheating" sorta kinda a little bit assumes an adversarial relationship between the GM and the players. But if you assume that the GM's job isn't adversarial but instead half narrator and half referee, then the idea of "cheating" against the players becomes simply inapplicable. That's why the comparison to being banker in Monopoly initially made no sense to me, because all the players in that game have an interest in winning, whereas the GM does not (or at least, should not).
What it does come back to, though (and I realise I'm rambling a bit, but I'm on a roll) is whether the players at the table value the journey over the destination (i.e., the fight over the victory). There is a mindset, which I think of as the "commando-unit thinking," that says "I will succeed by planning, accounting for every contingency, etc." From that point of view, changing the rules in mid-fight would feel totally unfair, because masting the system is at the heart of the experience. A one-shot victory would suit the commando-unit players just fine, specifically because it would signify that they had planned their attack so well that that's all they needed. If I were running a game with those kinds of players, I would not (now that I think of it) feel comfortable altering the stats on the fly. It would be anathema to their desired gaming experience. On the other hand, if I had a group that enjoyed the fight as much as, if not more than, the victory, then I'd be happy to extend it for their enjoyment.
It really does come down to preferred gaming styles and providing the kind of fun that people are signing up for, so the real challenge is making those preferences plane. Instead of claiming that this or that style is "better" or "more fun" (and projecting your own preferences outwards), you say "this is the gaming style I prefer, let's all agree on a style or a hybrid of styles before we start."