And that would be similarly clumsy in-play, or at least clumsy.
Except the Captain didn't hear the insult. He doesn't know what Mr. Insulty said. All he knows is that the BurgerMaster called him in. What the hell is he doing, talking about a conversation he hasn't heard?
So, we're moving the goalposts? Adding things to the story post-facto so we can say it should have worked out the way we think is "better play?" Because my understanding of the inident was that the audience was the BurgerMaster with a couple PCs who wanted to negotiate, Mr. Insulty, and Hostage-taker. After the insult the Burgermaster calls for guards, Hostage-taker tries to take the BurgerMaster hostage, and things go in a generally bad direction. How is it "deft GMing" to have character completely uninvolved in the conversation be the one to resolve it?
Bob and I are walking to the elevator, arguing. The doors open and Sam is standing there. Bob says, "I'm right, Sam, right?" Sam says, "No, prabe is right and everyone in the building knows it and also you're a nutjob."
I mean, that's pretty how you're describing the original incident with the modifications involved. PC's have audience with BurgerMaster; Mr. Insulty insults, as it says on the tin; BurgerMaster calls for the guards; Hostage-taker endeavors to fulfill his telos and fails; Captain comes in and says, "The PCs are right"; BurgerMaster curls up in a ball and cries. Meanwhile, around the table, the players are rolling their eyes as they realize they were supposed to try to suborn the Captain before talking to the BurgerMaster.
I don't think we disagree about whether TRPGs should be able to recreate common conversations. I think the descriptions of events have mutated so substantially that there's no clear understanding of which facts are being discussed, when. It's probably one of those things where Internet fora do not aid communication.