Looking at the setup, its just hard for me to believe her claim is true.

She claimed vig when DK was dead, and says this power can only be activated if a kill is defeated.

What are the odds? 2 vigs in a game of 12? Both using the same weapon? A gun? Not likely, there's a tendency amongst mods to try to vary kill style, not just as a marked path of destruction but also in the name of originality. Kills, especially of late, have tended to have a unique signature to them. I can't see him, especially since he is also a flavor text fan when modding, just giving two people the same NK path.

Personally, my thinking goes likes this:

Kylia poisons DK, gets the gun, and is informed of its properties. She knows nobody else has it and no one can say so since DK is dead, and knows vig is a safe claim because a repeat is unlikely, she fabricates a story explaining its non-use, not strictly necessary since a vig by general consensus isn't supposed to kill anyone on night 1.