And there were successful checks, or at least one, and the PCs that walked away walked away. That's how the OP described it. They just happened after the insult, which in the OP's telling didn't sound like any sort of attempt to alter the thinking of anyone. It didn't even sound as though it was an attempt to intimidate, to me.
Is part of this that you think the insult was an action, which should have succeeded? No, because you describe it as a failure.
It seemed to me as though that was narrating success by describing the actions of an NPC who hadn't seen the events in the OP's incident. Whom the PCs would not have been attempting to influence--could not have been attempting to influence. In spite of whatever the action declarations had been. If I say, "My character attempts to talk the Mad Tyrant out of executing Mr. Insulty," and you say, "The Captain, coming into the room, turns to the BurgerMaster and says (paraphrasing) 'I will not obey you, sir,' " I will at the least be confused as to why effect aimed at the BurgerMaster seems to have hit the Captain. You have (metaphorically) moved my hand from one target to another that was not there when I declared my action. That doesn't seem deft, it seems clumsy as hell.
It also looked to me as though there was some editing of the BurgerMaster--which is totally fine, even if those traits, et al. were maybe not entirely consistent with what I've gathered of the published adventure. I was, I'm afraid, engaged in a little light mockery when I invented similar tags for the invented NPC (the Captain) that made it easy to shift the events back in the direction of the OP's incident; the point, to the extent I had one, is that it is trivially easy to shift the story by rewriting NPCs, if you want to.
I think you're taking a strange tack, here, in insisting that only the target of an action can react to it and if anyone else does, it's redirecting the player's action.
Here, in
@Manbearcat's example of play, the player's action is to insult the Burgomaster. The stated goal this action is to force the Burgomaster to retreat from his campaign of forced happiness. The GM allows this to go to a check, which succeeds at the DC the GM sets. Therefore, the action must move the Burgomaster towards the goal of the player. However, the Burgomaster has traits that say he will react poorly to insults, so how to honor the success without abandoning the defining traits of the Burgomaster? This is the question
@Manbearcat is trying to illuminate: that this can be done; you can have a character act according to his traits and yet still honor the success of the player.
In this example, the Burgomaster reacts by calling for his Captain and ordering the PC incarcerated for saying his rule is weak. This is the NPC acting according to his traits -- we need to find the path to both allow this and honor the success of the PC action. To do this, the Captain, who, in this example is the Burgomaster's Bond (the Burgomaster respects the Captain), tells the Burgomaster that many in town believe the same, which is a blow to the Burgomaster's ideal that the townsfolk love him AND leverages the bond with the Captain to explain why the Burgomaster would even listen to this. Why the Captain chooses to divulge this information is not because the player's action was redirected to the Captain, but because this is a truth of the game (and it is, in the game's write-up, that many (most?) townsfolk think the Burgomaster's happiness plan is bunk) and the GM has decided to honor the player's success against the Burgomaster by reinforcing it with the Captain. This exposes the Bond (if the Burgomaster is listening to the Captain, clearly he has the Burgomaster's ear in a special way), honors the player's success (the Burgomaster is now forced to consider his plan is a failure), AND still honors the Burgomaster's flaw (he reacted to be insulted very poorly).
@Manbearcat's example has little to do with the OP situation in that it's not meant as an example of how things should have gone. It's provided as an example of how you could have played it -- how you could have had a PC insult the Burgomaster and still reached a success for the PC. That's it, and it does a good job of showing that. It doesn't redirect the PC's action, it honors it to the hilt -- the Burgomaster is insulted and calls for the guard! But it also honors the successful roll at the core of the example, but finding a way in the fiction to both honor the Burgomaster's written reaction to insults but turning that into a success for the PC by introducing the Captain as an ally to the PC's point.
Arguing this is bad play is saying that normal conversations, where people try to make a point against a recalcitrant other only to find sudden support from a third party, turning the discussion, is not something that you want your RPGs to be able to emulate.