what that content actually does in the fiction (i.e. how the chamberlain responds to the PCs) is derived in the moment - with or without the aid of any game mechanics - based on the PCs' words and approach.
What is the relationship between "derived" (the verb you use) and
decided?
In most RPGs the GM has to decide what a NPC does having reference to the PCs' words and approach: this is true of Classic Traveller, Moldvay Basic, Burning Wheel, Apocalypse World, Dogs in the Vineyard, Prince Valiant, and numerous other games.
A big part of what differentiates some of these games, in this respect, is the basis for the decision. Glossing this as "with or without the aid of any game mechanics" without considering the nature of those mechanics, who gets to decide whether they're invoked, in what way they take "words and approach" as input, and in what way they constrain the GM decision as output, seems to be overlooking the substance of the discussion.
For instance, just to set up three possibilities:
* The GM has no default disposition in mind for the Chamberlain, and decides how the Chamberlain responds by calling for a reaction roll by the player of the PC who approaches the Chamberlain;
* The GM has a note, or at the moment of play creates a (perhaps literal, perhaps mental) note that the Chamberlain is ill-disposed to the PC, and hence will accede to any request only if a particularly difficult social check is made;
* As the previous dot point, but the GM decides to "inhabit" the mindset of the ill-disposed Chamberlain and hence will have the Chamberlain accede to any request only if s/he feels that the player of the PC has made a sufficiently persuasive case.
Each of these is an example of
how the chamberlain responds to the PCs being derived in the moment - with or without the aid of any game mechanics - based on the PCs' words and approach. But I think it's obvious that they are very different approaches to adjudication.