yes, and he can just as easily grant it, so if one is denied, chances are there is a good reason for that
The "good reason" is solely in the DMs head and all the player sees is the DM, yet again, saying no to a granted ability.
Sure, it's all about trust, the players need to trust that the DM isn't simply out to screw them. But that's earned.
And the DM also needs to trust that the players aren't just making random hair brained requests, but are actively trying to engage with the fiction.
Which they will stop doing if the DM constantly nopes them for what he assures are "good reasons" (but, of course, doesn't show WHY they are good - that's not the players province).
And, I know, you say it's not constantly it's just THIS INSTANCE. But I've seen it quite often that the DM is so inclined to say no they don't even realize it's constant, they really think it's just a case by case basis.
I still am not sure why you rail against not getting an audience in the name of agency, yet presumably are ok with getting one in which all requests are denied. How does that result in more agency?
Because the ability as presented is at least met. And the DM can then SHOW the noble being an unmoving villain, or whatever. As opposed to not even granting the players the right to see it.
But also, things are fluid and players are creative. The DM may well go into the encounter expecting the noble to deny all requests but the PCs through great roleplay, lucky rolls or even unscrupulous magic change that outcome. It won't happen if the DM just says no from the getgo.