Concessions are not unilateral, they must be reasonable given the situation and are subject to negotiation to reach such a point, so it's not actually a given that a concession would offer this NPC the leverage necessary to avoid destruction.
It would seem to me, in fact, that, given the BCV's state, it would (or perhaps should) already have been the subject of a Taken Out result or a Concession, leaving it's fate in the hands of this divided party.