None of the big 4 Starfleet Captains would mishandle that situation by firing first, not even Janeway for all her faults. You do not fire first in a First Contact situation. Ever. If you die, you die, but you do not start a war on your own because you're scared. That said, turning the death of their leader into a justification to genocide an entire race out of existence IS the Minbari's problem (in the book, Earthforce even offers Jankowski to them as a war criminal hoping to stop the war, and in both the movie and book, Earth offers to surrender over and over). Specifically it's on the 5 (at least 1 other had to be Worker or Religious) on the Grey Council who voted for war instead of trying to figure out what happened, and especially on Delenn for voting to "kill them all, no mercy".