Yeah. I have a session to run in a couple of hours, and I don't need to be as cranky I'm clearly getting about this. The PCs have enough problems ...
I think that perhaps I and others aren't doing a good part of linking our points together because the answer to your question IMO should have been self evident.
The answer in detail is:
The insulting PCs action could have resulted in any number of equally realistic reactions from the NPC. The DM chose a reaction which then caused another PC to choose an action to attempt to take him hostage. So then we work backwards and see whose actions were justified.
If you've read the adventure, how realistic are any of those other options. The best one I've seen is a response that makes it clear further insult will not be tolerated (which I predict the player would then test, which would then lead to ... what happened).
The player that attempted to take the NPC hostage - were his actions justified? From a fictional perspective, I think so. From a game perspective - any escalating action that is in direct response to a direct threat toward a party members survival seems justified in the game to me.
I'm ... willing to go along with this, if the information was really so limited that he thought the call for the guards was (for example) to have the PCs arrested and not escorted from the NPC's chambers. There were, however, two other party members who didn't try to take the Burgermaster hostage, so maybe the call for guards was understood differently by the different players/characters? Differently understood does not mean unjustified, to be sure, but it seems to indicate the situation was not as clear as all-a-that.
Was the NPC's actions justified? From a fictional perspective, I think so. From a game perspective, a single insult in a peaceful negotiation should really not be leading directly toward something that can be perceived as a threat on the PC survival. That's where the NPC's actions fail to be justified.
See, I'm seeing it more from a fictional perspective than a game-ish one. The fact there's an in-fiction justification makes the actions justified for me. I don't think that makes those the only justifiable actions, of course, and there is something to be said for making sure the PCs know what the score is before they start doing stuff.
Was the PC's actions that insulted the NPC justified? From a fictional perspective, I think yes. From a game perspective, I believe they were justified because there is no indication that a single insult will directly lead to a threat to PC survival. In fact, given our analysis above it actually shouldn't have led to that at all.
I'm less sure about this. If the PC's plan all along was to use the negotiation as a ruse to get into the chambers and attack the Burgermaster, why not just ... attack the Burgermaster? What does the PC think he's going to accomplish by insulting him? It doesn't sound as though expecting it to make the negotiations go better is reasonable, and if he wanted to draw the Burgermaster into the fight why wasn't he the one to attack the Burgermaster? You can maybe make an argument that the player didn't have a clear picture of the stakes before he declared the character's actions, which is why I see the suggestion
@Maxperson made as reasonable, but it doesn't seem to me (based on what the OP said and my experience being at the table with that sort of player) as though that's likely to accomplish anything more than more insults.
Thus, I don't see any reason that we can fault either player for what happened.
And I do. I suspect this is where differences in viewpoint and experiences come into play. Among other things, I'm looking at this from more of a "makes sense as fiction" perspective and you seem to be looking at it from more of a "makes sense as (or makes good) gameplay" perspective. There's something to be said about gameplay, given that it's an actual game, and I genuinely appreciate that perspective, in spite of being cranky about this.