You know, now I'm not sure either. The first time I read the rules for concessions (ys206) I thought you couldn't use a concession to avoid taking consequences. Then I read it again last night before composing my response, and I thought it was saying that, as long as the target could keep going by taking consequence, then you can offer a concession instead. Avoiding the consequence by conceding the fight. It was only if the target had no way of continuing the combat, even with consequences, that a concession was unavailable. Just read it again, and I can't tell. I suspect that you're correct, the attack would have taken out the character, so the character's choices are to take the severe consequence, or be taken out on the opponent's terms.
If I were running that game, I'd tell my player what conditions I'm going to place on the Taken Out, and then let him decide whether to take that Sever Consequence and keep going, or accept the Taken Out as I described it. So whether or not the wizard's Third Eye is still open in the next scene would still be negotiable, just with the GM in a stronger negotiating position. I think coming to a consensus at the table with the players about where the narrative is going next, what makes the most sense, what's going to be the most fun, is probably your best course of action, 9 times out of 10. Anyway, that's what works with my group.