Things can get weird because a lot of Narrativist best practices aren't actually best practices and what gets ported between games is obviously reliant on the group.
The three most influential games on Narrativism used to be Sorcerer, Burning Wheel and Inspectres. They all had different approaches and it's only Inspectres that is full on Narrativist in the way people often imagine.
The InSpectres system is both incredibly easy to learn and incredibly challenging to
use. The basic gist of the system is this: roll your skill dice when you want to use a
skill, compare the result to a chart, and carry out the instructions on the chart.
To do this, roll a number of six-sided dice equal to the number listed beside the skill
you’re going to use. So if you need to make an Academics roll and you have an
Academics of 3, you’d roll three dice. That’s all there is to it.
After you make this roll; you’re going to have a handful of dice with numbers ranging
from 1 to 6. Find the highest number shown and compare it to the Skill Roll Chart.
Skill Roll Chart
6: Amazing! Describe the result and gain 2 franchise dice.
5: Good. Describe the result and gain a franchise die.
4: Fair. Describe the mostly positive result of your action but you must also include a
negative or humorous effect.
3: Not Great. The GM decides your fate but you may be given a chance to suggest a
single positive (albeit minor) effect.
2: Bad. The GM decides your fate or you may suggest something suitably negative.
1: Terrible! The GM gets to hose you with a truly dire situation resulting from your
incompetence.
This might seem a bit strange if you’re an experienced role-playing gamer. Yes, you
read it right. You get to call the shots if you’re successful. The idea is not that a high
roll results in a successful use of the skill. A high roll simply means that you, as a
player, can take over the game for a bit and describe the situation however you like.
It stands to reason that with this amount of power, you’ll use it to your advantage,
right? Or maybe not! Nothing is more fun than hosing your own character…
And even if you don’t roll well, it doesn’t mean that you failed! It just means that you
have to put your character in a tough or tense or comical situation. Your character
doesn’t miss the vampire with the stake, you hit it in the stomach instead…or it’s not
the kind of vampire that is killed when it’s staked…or anything else you can think of.
It’s okay to “lose,” because the game is not about “winning” (besides, a failed roll is
just a temporary setback and not a carved-in-stone result of, “OH MY GOD, WE’RE
TOTALLY SCREWED NOW!”).
Inspectres has exactly the problem you mention. How does the skill relate to the results? Well it doesn't.
Sorcerer was the game that coined conflict resolution. The stats in Sorcerer are Will, Stamina, Humanity, Lore and Cover.
The dice are rolled when someone does something that prevents/conflicts with what someone else is doing.
So Elric the thief has alerted the guards and is trying to get away from them by picking a lock to this heavy door. He wants to get through and slam it behind him. The guards are trying to get to him first.
Whether he can pick the lock at all is determined by his cover. If he can, then the fictional results are really about the guards speed V his speed at picking the lock. So skill kind of plays into it but skill is conceived of as a mix of keeping cool, speed, knowledge, whatever else might be in play in a given conflict.
Later on we have Apocalyse World and Blades in the Dark. A lot of how Apocalypse World is played was influenced by Inspectres for a variety of reasons (Narrativists have a habit of trying to play every game like it's Inspectres). I play it more like Sorcerer.
So Midnight is trying to get to the safe but the staff of the house might find her. That's an act under fire roll with the fire being 'she's spotted'. Why is she spotted, well it says right there in the text 'it would mean she hesitated, wasn't quiet fast enough, and so on.'
So on a success it's not that there isn't a cook but that we probably wouldn't describe the kitchen scene but instead go straight to her arriving at the safe. If we were resolving at a lower level of granularity then we'd have to decide if the cook is there. Like I could frame the scene:
You're sneaking through the kitchen and you hear someone coming (I'm thinking the cook). Midnights players says she's hiding behind whatever. We roll. failure means she fails to hide because she either wasn't fast enough, didn't find somewhere to hide, something like that.
Let me bring up this part didn't find somewhere to hide. We can interpret that two ways. One is that the dice roll failed to conjure a place for her to hide, the other is that she wasn't quick enough in her evaluations to find a good hiding place.
What about in D&D, what would a hide roll look like? I mean if we're being ultra strict there is either a place to hide or there isn't. I think it would probably work the same way in a lot of D&D games as it would in Sorcerer or Apocalypse World, it's simply not that relevant. In all three games the GM can flat out say 'there's no place to hide.' SO A ROLL ISN'T POSSIBLE.
But what about Burning Wheel? Well there's what the texts says, what Narrativist culture has passed on, and how a given group plays. This create a weird mix.
IF we take 'say yes or roll the dice' in a very literal sense. Then the GM isn't allowed to say I can't hide, they must say yes, so there IS a hiding space. Unless they make me roll.
Do you see how Burning Wheel now becomes Inspectres and how if you port this advice, all Narrativist games start becoming about who has content authority?