As much as I try and present a story for the players to help flesh out though, I keep in mind that this is a game. In all but the most extreme circumstances, I let the dice "fall as they may", and try not to twist the rules simply to accommodate my story idea.
As it turns out, I think letting the dice fall where they may makes for a stronger story experience. One of the challenges for writers of fantastical fiction is making the world and characters feel real enough for the readers to invest in (aka verisimilitude). When writers talk about creating and preserving verisimilitude, they actually use phrases like: "Your world must be consistent; don't break its internal rules!"
When you fudge a die roll or pretend, "Well, ok, that will work this time," you're damaging your verisimilitude. You're weakening your story. (Likewise, when you whip out your story points to change the rules temporarily, you're weakening verisimilitude unless those story points have actual existence within the world of your story. This is why I can't enjoy most story games; they actually have mechanics in them that damage the story!)
But when you apply the rules of your game consistently, you strengthen the verisimilitude and you make the story more enjoyable. When players know how their magic works, or how likely they are to defeat a troll, or how the city guard will react when they discover a pick-pocket, they can invest emotionally in their characters and the world they inhabit.
In short, if you want your RPG sessions to have the effect of a story (rather than just mimic the structure of a story), you need clear, understandable, and consistent rules. (It’s not all you need, but without them you’re not even going to get started). This is also why it’s important that the rules you choose actually promote the sort of story you want to tell. If you’re fighting your rules, you’ll constantly see your story drift away from the look-and-feel you were aiming for.