Your answer is kind of insulting. I mean we are using dice to adjudicate something happening in the world. That is a far cry from the DM giving the player the choice whether some random event is going to happen to their character. It's obviously not something the character even knows about. Lumping that kind of thing in with rolling dice to hit which the character is attempting to do is disingenuous at best.
I apologize for my flippant tone. Re-reading it does indeed come across as insulting. I meant to try for an absurdist/humorous tone, but, yeah. I failed. My player must have rolled low, or accepted an intrusion ... anyone, sorry, and thank you for only a gentle rebuke.
Anyway. We have a player trying to have their character do something. Case A is the player rolls a dice, consults his character sheet, does some math and gives a number to the GM. The GM then says how well the attempt succeeds. Case B is the GM asking the player if they wish to simply succeed well, or accept a less successful result with a player reward.
In neither case is it "something the character even knows about", so I do not see that argument has any validity. In both cases the character attempts to climb a wall. They fail and get hurt as they fall (or suffer some other sort of mishap). The character cannot tell why they failed. In case A it is purely a gamist reason. A roll of 20 would have succeeded, a roll of 1 failed. In case B it is purely narrative reasons. A boring intrusion would have been rejected, an interesting one accepted. In both cases simulation was used to set up the parameters (the fail % for the gamist case, the possible intrusion in the narrative case), but it's basically DICE=GAMIST, INTRUSION=NARRATIVIST.
I would actually argue that the narrativist approach is more immersive, whereas you argue it is less immersive. And the reason is that for the narrativist approach all I have to do is think about my character and what makes sense. I stay in the story, in the mode of thinking about my character. I don't even look at my character sheet. No external polyhedra, numbers, statistics on a sheet, or anything distract from being immersed in the experience of my character.
In both cases the PLAYER is using some decision process to decide what happens to their character. Game mechanics or narrative, their CHARACTER has an outcome based on that process.
If you straight-out dislike narrative elements, then of course you won't like it! No problems with that at all -- what I do feel is not accurate though is the attempt to say that dice rolling is inherently more immersive. It may jar you, because you don't like narrative style. For another person, it may be more jarring to have to pull out a book and work out what the penalty for climbing walls in the rain is.
Personally, I like a mix. And I like mostly simulation / gamist decision making -- rolling dice, following rules, etc. But I do like a bit of narrative in here and there. Not MOST of the time (I do actually like Fiasco, but cannot play it a lot ...) but definitely occasionally.