Yeah, his response looks at first glance as though it contradicts the RAW, which states:
Finally, a character cannot be saved from a roll that takes him out by offering a concession. You have to offer the concession before the roll that takes out your character. Otherwise, it’s cheating the opponent out of victory.
However, at ... oh, around fourth glance (at least in my case), I came up with the following parse that seems to fit both RAW and those comments:
Before an attack is rolled/resolved: You may conceed
only if the attack has to carry the potential to inflict enough stress to take you out -- exceeding your stress track, though not necessarily taking into account available consequences, since you can choose not to take them. Note that since there is no explicit "roll to take you out" in Thaumaturgy, the decision is made at the completion of the spell (but before it is resolved).
After an attack roll/during resolution: If you have enough remaining consequences to avoid being taken out, then you have a choice between taking the consequences or offering a concession instead of taking the consequences. However, if enough stress results that you can't stay in the fight even if you were to take all of your remaining consequences, then you are taken out without the option of concession.
This satisfies both RAW and Fred's comments. So in the case of Thaumaturgy, this means that at minimum, the spell has to be set up to inflict stress enough to exceed your stress boxes (but not your consequences). If it does less, then there's no option to conceed.
As to the scenario in question, I don't see any reason why one player can't offer a concession when other players don't. As long as the concession is deemed
reasonable by the table/GM, then go with it. And if another player wants to duke it out to the bitter end, then that's fine too. The player who intends to conceed just starts using his actions to set up for the concession. I think it's probably a good idea to rule on whether or not the concession is legitimate before going on; if not you should gently point out that there's no way to simply "escape somehow" the massive death spell that will eradicate all life within ten miles, and ask if they'd like to try another option.
If you'd like to look at it another way, the 'escaping' player is basically using his actions on an extended contest to get out of the dead zone. You might take this option literally, saying that he has X exchanges to achieve Y shifts worth of sprinting in order to get away, or you could handwave it and say "Sure, if you clear out now, you can get away ... especially since your buddy Bob is sticking around to keep him busy."