In the campaign my Black Garb does not kill the Pillaging Arsonists after they deal combat damage to my hero. Neither of the two card's text indicate why this would be happening.

Black Garb:
"When an ally deals combat damage to your hero while Black Garb is in play, that ally is killed."

Pillaging Arsonist:
"At the end of each of your turns, all allies without Outlaw alignment take 1 fire damage."