I assumed he convinced them that letting him out was actually a good idea, in-character, and then pointed out the flaws in his arguments immediately after he was released. It's entirely possible if you're sufficiently smarter than the target. (EDIT: or you know the right arguments. You can find those in the environment because they're successful; you don't have to be smart enough to create them, just to cure them quickly.)

EDIT: also, I can't see the Guard accepting that deal in the first place. And isn't arguing out of character against the rules?