For Jackpoint or some other (any other) professional network, I'd actually expect the opposite. If it's in the middle of a job, you should pause, nod, and let the other guy live - even if you don't let them get away with the goods - so that they can continue to contribute to the good of the network, and even to continue to spread your rep. If they start gunning for you, though, and they keep doing it and make it personal, whether or not you hunt the fragger down, once you have them there, you burn them to the ground and salt the earth their ashes cover - they made it personal, and since you get the chance to finish it, you finalize them with just the sort of extreme prejudice Michael Chandra suggests.
Business is business, you act professional, and you give the other professional a bye. If they make it personal, you don't go all noble; the guy threatened your kid. No safehouse on or off the planet would keep you safe from my wrath, you did that to me.