In retrospect, it does seem like a blowhard move, especially for a diplomat.
Let's add it up, in terms of infractions against the other nation:
Kirk, essentially, killed 8 or 9 Klingons when he blew up the Enterprise, shot another one on Genesis, whom even if it was on stun, ain't nobody was worried about him when they all beamed up, and then gave Kruge the boot (literally!) In all, Kirk killed eleven Klingons and stole their ship.
Opposingly, we have no clear indication in Star Trek III that Kruge was acting under orders from the Klingon government, do we? It's just as likely he had gone rogue trying to prop himself up by winning a victory or two against the enemy. And even if he had been under orders, it's a pretty bad negotiating point to be playing victim when you sent your guy out and he destroys one ship, killing it's entire crew, and later orders the outright murder of a civilian (David).
I too, fail to see the logic of the Klingon Ambassador's argument in IV, and would cheer Sarek all the more for calling him out on his bullshit, had the argument not been so logically and empirically stacked in Sarek's favor.
Then again, maybe the Klingons did want to go to war after all and had just sent Daddy Warbucks to stir shit up.
