No, this conflates a narrativist agenda with no myth / heavily improvised play, which is not at all a given. I'm not sure if you're also implying that in the narr game the player is inventing a solution to an in-game mystery.The real difference between a simulationist and narrativist focused game using that feature is this.
A simulationist DM will have made a note already that the Duke of this region often travels during the summer, and as such won't be in their estate to receive an audience from May to August. Despite not being able to use their class feature, the simulationist player is happy because it demonstrates that the campaign world has details that exist beyond the scope of the character.
A narrativist DM will make up the name of a Duke (unless a name is already in play due to previous framing), and introduce the next scene where the character can meet the Duke. The narrativist player is pleased because he knows this Duke was part of the conspiracy that unjustly murdered his father, and he can finally confront the foul murderer.