Hiya.
Can a DM "cheat"? Hmmm...yes, sort of. Ex: Player says "My character leaps across the pit!"...DM replies, "Hmmm. No. You don't. I don't want your character to do that." That is cheating because the DM is breaking the rule that the PC is under the players control unless something else is at play (e.g., controlled PC or somesuch). Other than that...no, not really.
That said, players
can feel cheated. Quite easily, actually.
Having read the OP's initial post, for me, if I were a player in that game...yeah, I'd feel cheated. If the DM is looking at a monsters stats and it says it does 1d6 with a claw, but then the DM announces "You, PowerCheracter#2, takes 10 points of damage" because PC#2 has lots of HP's compared to the other's...that's bad. That's one of the worst things a DM can do, IMHO; change rules based on "whim" because the DM is under some sort of delusion that "his story trumps all".
So, here are some specific points I'd like to, um, point out, that may have given the players the feeling of "being cheated".
The campaign was such that the player characters were grossly imbalanced (as I allowed the players the freedom to play whatever type of character they wanted to play) and I often made things more difficult on the player characters who were the most powerful.
Ouch! If an average monster is fighting the PC's, and said average monster is significantly weaker when it attacks the weak PC, but it is significantly tougher when it attacks the strong PC...that's pretty close to dead on "DM is cheating" material. A monsters AC, for example, should remain constant...not go up or down based on whom it was fighting.
But as I said, this game was not about power or balanced combat. In fact, combat was a side-story, usually limited to climactic, cinematic-style encounters
Then why "fudge" dice in the first place? If combat was secondary, so what if Player A has a helluva time, while Player B walks all over everything? If the characters and the stories were that engaging and important, then that shouldn't matter. I've had players of both extremes in my campaigns at one time or another. The "storyteller" player could care less if the "powergamer" player was kicking ass, and vice-a-versa. If the system is at fault (which I think you mentioned), change the system...don't change the rules willy-nilly, character to character.
My opinion is that the story trumps rules (and dice) all the time unless the campaign is specifically designed as a tournament-style challenge.
This tells a lot. Obviously, to the two players, "story trumps rules/dice all the time" is a deal breaker. I think that they may have been ok with it if it "wasn't so obvious" to them. But it was obvious you were "fudging" numbers all the time. Rules are there so players have a baseline expectation of how the world works. If the DM is going to "pick numbers" to balance everything out, then why not just have everything be a simple coin toss? If a player invests heavily into a characters combat prowess, he *should* expect to be significantly better than someone who didn't put much of anything into combat prowess. To do otherwise is to cheat the player out of his expectation of play.
^_^
Paul L. Ming