You're right about "background briefing." You don't go "on background" (or off the record) with a pool of reporters present.
But now we get back to the Predator! GREAT! THE PREDATOR WILL SAVE US!
Fox had permission to release the "background" - and background is not "classified". Kerrey was way off the mark - it was just the typical knee-jerk reaction from the typical democrat jerks re anything Fox says!