What was this paladin's alignment and oath supposed to be? While I don't dictate character choices, if it was supposed to be the LG type, I would probably have mentioned something to give him the idea that the action he was contemplating might not be a good fit for his alignment/oath (in my campaign, that sort of thing affects what happens to your character after they die, and having a little scene with dead characters can be interesting so they can see where they ended up).
In any event, I get the impression that this player wanted to play a jerk character. He started a fight because he was a sore winner? Seriously? It also sounds like the DM telegraphed everything thoroughly, and that the consequences were naturally arising from the setting and scenario. The only things I can see that the DM did wrong are perhaps not giving the player a Session 0 recap, and saying that he killed the character in the thread title. He didn't, the player was role-playing a jerk character (which may or may not have been making a mockery of his declared alignment/oath), he was warned of the likely consequences of his actions repeatedly, by both the DM and the other players, and he still chose to take the serious risk--which wasn't even an automatic fail.
If a DM were to artificially save this character from his action's natural consequences, and I were a player in that campaign, I would be seriously reconsidering if this is a campaign I want to play in. Saving jerk characters who choose to risk their lives to be jerks would be no more desireable in a DM than arbitrarily killing characters because he doesn't like them.
My judgement is fully in favor of the OP on this one.