See, but here's the problem.
What do you do when the player rejects the DM's narrative. When the player finds the DM's post hoc justification to be not simulating the world?
For example, let's use the rope example. You talk about the rope being cut by a rock. Now, I've done some climbing with the army. I know pretty well that no, any rope that is strong enough to be used for climbing is not going to be cut by a sharp rock. At least, not accidentally. Unless your rocks are made of diamond (or perhaps obsidian) it's just not going to happen. You cannot cut a 3/4 inch rope with a rock. Not going to happen.
But, the DM thinks it's perfectly plausible. The DM thinks that this is totally normal and can be done.
At this point, the simulation is not functioning. The only way it works is if the player must accept whatever the DM makes up at the time. Which, in cases where the player may be more knowlegeable than the DM, means that many times the narrative isn't possible from the player's POV.
Unfortunately, there is nothing to resolve this because the mechanics provide no information.
If they don't accept it then they need to either accept the limitations of the game or find a different game because they want something I don't. If you want a mountain climbing simulation, D&D isn't for you. Personally I don't know what it would even look like because as soon as you figure that out then you'll have figure out tree climbing, scaling a castle wall, a giant beanstalk, the giant furniture you find and occasionally a giant. Then you have to have a swimming simulation, be able to calculate exactly how far you can swing from a rope. The list of abstractions is endless.
I don't care about that level of detail because I don't see why an author of the rules that doesn't know the current situation can do any better. All simulations use abstractions that don't go into granular detail I don't see any value in a game attempting to go into detail when it can't possibly do a very good job of it.