@Leo.
I guess I should have said "A good DM knows when to ignore the rules and the dice rolls, but ignoring them doesn't make them a good DM or it a good adventure". The players do deserve a good grounding in the game-world and mechanics of it, otherwise it ends up as you said, an experience of enforced storytelling. There is also the matter of outcome of the successes and failures of said dice rolls. A good description of what happens does a lot more than saying "You lose 2HP."
It's one of the challenges of DM'ing to "assist" your players through your adventure, and one that can go horribly wrong. Things like actual adventure mac-guffins compared to basic descriptive wallpaper often do get mixed up. So there's a few (dead) skeletons by the entrance of a troll cave? Well, they were probably there for scene-setting and maybe a loot-pile (I'm a lazy DM on occaision). But when an entire play session ends up with your characters searching for items, identifying them, talking to said skeletons, raising them, arguing about whether raising them is "righteous", equipping skeleton minions, then running away from the cave because there was rumbling and growls coming from inside, it can be quite annoying. They were just meant to see that the cave was a bad place god-dammit! In the end the players did go into the cave, because I "invented" an orc hunting group patrolling the area, a big one. Better the devil you don't know than 20 orcs you do know about.
Sheparding players is fun, but sometimes difficult. Doing things on the fly is a pretty necessary part of it. But believe me, they were all going to die if they didn't go into that damn cave by the end of that play session.
In the imaginary example of the pit jumping, it depends on just how necessary it is for the players to go down there. Piquing player interest in areas is very important (although, as said, can back-fire). Maybe they noticed a glimmer of something shiny whilst jumping across? Maybe they could hear noises coming from the pit? Maybe the player got grabbed by the monster, even though the jump would have been successful. Just saying "well, you didn't make the jump", even though they obviously did, is a bit harsh. But descriptive outcomes can cover a lot of that. Hand wavey explanations sometimes have to work. But sheparding players through interest or fear of death often works as well, better in my opinion. But as campaigns continue and characters get more flexible and powerful, I reserve my right for hand-waving. I'll let them happily destroy a perfectly set up scenario with spells and items, letting the players do whatever they want, as long as they don't mind me killing or maiming them all whenever I get sick of them faffing about.
As a good example of descriptive outcomes and player sheparding, have a look at Einsteinian Roulette on this board. That roll of a 3 can mean lots of things, even if it's just below average. There's a game-system at play, but the outcomes can be very different from what you expect. It does make for a great adventure however. The players still feel "reasonably grounded" in the rules and their "rights" within them, but there's a huge array of outcomes available for any action (like being horribly injured mostly). Pity I had to pull out due to time constraints. I never get time to bludge around on bay12 any more.
I do find 3.5e a far easier format for "complicated" situations than 4e is. It has just enough RPy'ness that you can resolve all kinds of things that are only marginally in the rules (or originally planned to be in the adventure) "fairly" for the players. There's nothing saying you can't do all that in 4th, I just find 3.5e easier to do it in.