actualy, googled republic side Kaon video, you are correct too.
weird republic ways are... weird.
I always found the faction differences odd with this decision.
Even the paraphrase on the wheel is different. For Empire, you get something like "End his suffering" (LS points) and "Watch him suffer" (DS) while on the Republic side it says "Kill him" (DS) and "Let him live" (LS) even though the outcome is the same (you either end his life or stand there and watch him turn).