Balesir
Adventurer
Not quite; (c) says the DM rolls, not the player.Which c) is, in a nutshell.
I actually think the flaw in the poll is bigger than this. There is an additional (missing) option where the non-combat situations become a mini-game constructed using tools and elements provided by the game rules, and the players are 'invited' to engage with the mini-game (just as they do with combat). The "players engage the world" option I have found, through long experience, to be conflicted, because the game world is only extant with full fidelity in the DM's head, and yet the players are asked to engage with it (in "traditional" RPGs) without being given any knowledge or control over it. With a mini-game, at least the elements are explicit and understandable by all involved.