"Doctor! It hurts when I move my arm like this!" "So don't do that, then…"
On page 168, the rules discuss what it means to be "Taken Out" — and, in particular, what the circumstances are like in groups where Taken Out equates to "dead":
So, if you think about it, there’s not a whole lot keeping someone from
saying, after taking you out, that your character dies. If you’re talking about
a physical conflict where people are using nasty sharp weapons, it certainly
seems reasonable that one possible outcome of defeat is your character getting
In practice, though, this assumption might be pretty controversial
depending on what kind of group you’re in. Some people think that character
death should always be on the table, if the rules allow it—if that’s how
the dice fall, then so be it.
Others are more circumspect, and consider it very damaging to their fun
if they lose a character upon whom they’ve invested hours and hours of
gameplay, just because someone spent a lot of fate points or their die rolls
were particularly unlucky.
We recommend the latter approach, mainly for the following reason:
most of the time, sudden character death is a pretty boring outcome when
compared to putting the character through hell. On top of that, all the story
threads that character was connected to just kind of stall with no resolution,
and you have to expend a bunch of effort and time figuring out how to get
a new character into play mid-stride.
That doesn’t mean there’s no room for character death in the game, however.
We just recommend that you save that possibility for conflicts that are
extremely pivotal, dramatic, and meaningful for that character—in other
words, conflicts in which that character would knowingly and willingly risk
dying in order to win. Players and GMs, if you’ve got the feeling that you’re
in that kind of conflict, talk it out when you’re setting the scene and see
how people feel.
At the very least, even if you’re in a hardcore group that invites the potential
for character death on any taken out result, make sure that you telegraph
the opponent’s lethal intent. GMs, this is especially important for
you, so the players will know which NPCs really mean business, and can
concede to keep their characters alive if need be.
The Rules As Written answer, therefore, is that the GM has made a poor choice in setting the stakes that way, and should reevaluate the desires of the NPCs in question.
However, you're asking who bends when the unstoppable force meets the immovable object. In this case, the rules strongly suggest that the GM does -- the ability of the player to concede in this circumstance means that if he or she wants her character to survive, the character does. It's up to the group, as you quote above, to come to a consensus about how this happens.
In the situation you describe, I might have the bobcat-people maul the character and leave him for dead, rendering him wounded but capable of recovery with medical attention later. But at any case, once the decision is made to concede, it's a good time to stop and check in to make sure all parties are on the same page regarding the story being told here.