Correct! The information asymmetry drives the whole thing. I think that's part of what makes it challenging for people (myself included) -- we're conditioned to see problems involving probabilities as involving *random* selections because that's how probability classes are taught
I've apparently gaslit myself about the monty hall problem since learning about it 10 years ago!
The entire thing hinges on the fact that he knows which door has [desired object] and he will never open that door! That's the only reason it's probabilistically best to switch