But, what about the third option DM.
The DM that insists on a narration AND a die roll? Because, IME, that's generally what happens whenever someone calls for a check. The whole "well, if you naughty word your way through well enough, you won't have to roll" never seems to happen. And, again, I'm sorry, but, I simply don't care to make the DM "comfortable". That sort of Mother May I stuff just drives me up the wall. Particularly, again, this is my experience, no matter how detailed and "good" the narration is, it's always going to come down to a die roll anyway.
My approach is to stop wasting the table's time. If the narration isn't going to impact the die roll in any way, then narrate AFTER the die roll. I far, far more want the DM to simply ask me what I'm trying to achieve. What is my goal. Then he can tell me how I can do that. I have zero problem with that at all. Which, frankly, is exactly how I handled the situation at the time. I just told the DM that I wanted my character to climb that wall. I had no idea how I could achieve that, so, just tell me what I have to do and I'll do that.
I really strongly dislike the notion that I have to jump through hoops to make the DM "comfortable". The player has told the DM what the player wants to achieve. Just tell the player what to do. What's the point in the back and forth? IMO, it's far more productive if players simply tell me what they are trying to achieve and go from there. The how is largely dictated by the die roll AFAIC.
Player: I want to search the room to find if there are any secret doors.
DM: Ok, make a Perception check (or Investigate, I'm not picky).
Player: 17.
DM: You search the room, looking high and low and discover ______.
The whole, "well, did you search THIS spot? What about THIS spot? How about THIS spot?" thing just makes me want to stick a pencil in my left nostril and push.