I'm not sure that anyone can object to any character taking a concession in a conflict. But basically, as I understand it, the idea is that for a character to really fall into temptation, the step to do so must come from free choice, not from being tricked into it. As such, I would never use a concession to cause a PC to kill a character they didn't intend to kill.
One option you might want to consider, which is something my group does sometimes, is when a physical conflict starts, get an idea of everyone's intent. So the players get to know if their opponents are going to kill them if they win, and they also need to make the decision right there if they're going to pull out all the stops.
Now, compels are a much different story. If a PC takes someone out in a physical conflict, and you want to see whether they'll cross the line or not, offer them a Fate Point and compel an appropriate Aspect. That's much more in keeping with the way the system's designed, and the player can feel like you're just heightening the drama rather than trying to catch them out.
Granted, I get a very strong vibe of "don't take the p*ss" with this game. Sure, the players could fling fireballs and gunfire around, and decide "no, I'm not killing anyone" all the time, but that sets a very specific, light-hearted (or even comic) tone, which isn't appropriate for every game. It's the responsibility of everyone, player and GM alike, to make sure everyone's on the same page.