Were you invisible while conning? You will always con indifferent to mobs that cannot see invis while you are invisible.
From my understanding, you need to be on the mob's hate list to get faction hits when they die. So removing yourself from the hate list in some manner before the mob dies would cause you to not get faction hit.
As a simple example, if you DoT a mob, and Feign Death right before the mob dies from the DoT, you will not recieve faction hits when the mob dies.
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