Sure. Really it's about what work the system does and how different systems do different work. In 5e, it's no controversial at all that the orc is hit and that this bit of fiction is the system's say, suggested by the player and described by the GM. This is normal. When it's applied outside of normal, like outside of combat, it's weird because 5e doesn't have the system have a say here. But, in reality, the difference is not one of kind -- the player suggests an outcome, the system says who gets the say, and the GM describes the outcome accordingly. Constraints are different, but the function of the game, the actual play, is the same.
I'm pondering, and I think it feels weird to me to have a player rolling/declaring where a person IRL doesn't have impact on it. So a roll for determining how positive a social interaction seems ok to me because I'd like to think what a person does has an impact on social interactions. A roll to see if a character is able to solve an engineering problem seems ok to me because I'd like to think the effort and training a person has would have an impact on that. A roll to find a forge that exists seems ok to me because I'd like to think peoples effort and luck determine whether they can locate things.*
It feels different to me to have the DM (as an oracle checking procedure; perhaps using dice perhaps not) consult a (maybe not yet fully rendered) mental-map to see if a forge exists, than it does for me as the PC to have the forge come into existence because I want it to. I'm imagining a twilight zone episode where the world the main character hasn't seen yet doesn't exist until they go look. Say the main character is looking for a store of some sort - it feels like a very different episode to me if the show has the between-the-seconds craftsmen building out what's there according to some pre-made plan, vs. them listening in on the characters thoughts and altering the plans based on what the character in the show wants. Or it feels like a very different theological world view to have a world created where humanity can "succeed" if they all work together and do the right thing, vs. a world where the divine decides each day to nudge things against whatever rules of science others might see and miraculously reward/punish folks based on what they've done.
There is of course a tension there. I'd like for the world I'm exploring to have things interesting to my character in it - and not be too real life in terms of the random bad stuff that seems to happen in terms of drudgery and pain and set backs. And so I do want the DM to have built (or be rendering) the world based on those general desires.
So maybe a better example is a Star Trek:TNG episode where someone wants to go in the holodeck to experience what a well trained explorer might experience on some planet, specifically in regards to discovering ancient ruins. They call up that program and go have some recreation time. It feels like a very different holodeck program if the holodeck is generating parts of that planet full of interesting things at an appropriate difficulty level for the crew member to go check out and the crew member wondering if they'll see something in particular or not, as compared to a holodeck program that takes verbal cues from the crew member about what it should generate around the next virtual corner.
Or similarly, when one starts up Minecraft there are a lot of options and mods to set what is in the world before you start playing so that you're pretty sure you'll find interesting things. And then you can go off in survival mode and see what you can find. Or you can set it on creative mode and hit a button or type a command to have the game spawn whatever you want if it wasn't there. Survival mode seems very different from creative mode.
Is creative mode weird to the survival mode player just because it's not survival mode (because the creative mode things weren't in the survival mode rules)? Or is it because there's a difference in kind? Where would a "stochastic creative mode", where you can try to spawn things in parts of the screen you hadn't seen yet, but there's a chance of failure, fall?
Edit:
* Disclaimer: I'm trying to think of who I have roll if the player is shopping and wants to see if a certain thing is in stock or not. I certainly have had the player roll instead of me sometimes if I was ambivalent, but didn't want the store to just become magic Christmas land. In other cases I might say it is just there or just not there based on how I picture the store. That feels somewhat akin to having a table in the book that gives what percentage chance each thing is in stock - and if such a table were there (instead of being generated on the fly in my head), I'm not sure if it matters if the PC rolls or the DM rolls. So the forge thing isn't that totally out there. But having all the locations be completely random feels different to me from having some that would certainly have it, some that certainly wouldn't, and some that might. If forges are a common occurrence, then a big chance of having it in that hex seems great. But if random forges in the woods are rare, then the chance should be small. --- The key to being a Bayesian is how the prior is set, and in many cases it makes all the difference.