I know I'm weighing in late in the game, but I think an important element is that the players need to feel like you, the GM, are on their side. I have been in very adversarial games and they are no fun. But when I'm playing a game and I feel like the GM and players are telling the same story, then there is a lot more that can be done and accepted. This can work even for "seeing what happens" sorts of games. The players still need to feel like the GM isn't out to get them, but is even rooting for them.
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.