I'll elaborate on this example: the DM could also decide that, no, there's absolutely no way this monster would be afraid of this character's antics. No roll, no intimidation. It's right there in the rules.
Now, the rules don't actually provide any guidance on how to handle the inverse situation. It may not be provable, but it's certainly reasonable....again, given the text on 185....that in the inverse situation the player is the one who adjudicates the effect on their own character. The DM gets to do that for the entire rest of the world, but the Player has authority over their own character. So if they say, "Nope, no chance," there's no chance.
Again, not RAW, but in my opinion (and it should be
@Lanefan's!) that seems more logical than saying, "No, the DM gets to both declare NPC actions
and adjudicate their outcome, even if it involves PCs."