(Updated title per suggestion in comments. Thanks, thelatinist!
That;s right: Fox is claiming that the Army's statement of "thanks but no thanks" to this hypocrite is, in essence, admitting that he's right. That he doesn't have to deploy.
As any thinking person can surely see, he volunteered to go to Afghanistan in May as a publicity stunt. He'd already joined forces with Orly Taitz in a lawsuit for which the tireless wingnut had been seeking military types. She found what she was looking for in Cook: a wingnut willing to trade his (reserve) military career in exchange for some 15 minutes of fame in a Quixotic quest to get their out-of-right-field seen in the light of day.
But now Fox News is carrying it one step further: the military sees through his ruse, basically says they aren't interested (I mean, they might not have been all that interested to begin with--he did volunteer, after all, rather than "answering the call" after the military had pursued him). But Fox characteristically spins the military's rejection of this particular nutcase as acceptance that his claim actually has an iota of value. Classic.