Yes, that's exactly what I was thinking. General Broadwings thinks General Derpy is bluffing, so Derpy credibly precommits herself to not releasing him by telling him information that would surely doom her army if she did. She gives up the choice of freeing Broadwings, and comes out ahead for it.

It's kind of reminiscent of this, from pages 43-44 of the 1980 edition:

It is not always easy to make a convincing, self-binding, promise. Both the kidnapper who would like to release his prisoner, and the prisoner, may search desperately for a way to commit the latter against informing on his captor, without finding one. If the victim has committed an act whose disclosure could lead to blackmail, he may confess it; if not, he might commit one in the presence of his captor, to create the bond that will ensure his silence. But these extreme possibilities illustrate how difficult, as well as important, it may be to assume a promise.

Compare also Daniel Ellsberg's Kidnap game.