Seriously... You'd think of all the billions of dollars that go into military training they'd be able to put up a few bucks to teach this guy how to lie a little more believably
The guy probably hasn't had to worry about such things for decades. He's an operations bureaucrat, and probably someone above him decided they could afford to burn him if the shit hit the fan (and by this point, they probably already knew some shit was heading toward the fan).
More likely: He, and everyone else involved in this, know that it doesn't matter if everyone knows the answer is a lie - the likelihood of any negative consequences is pretty much zero. First, the odds that anyone will be able to provide sufficient proof to cause any problems is minimal, secondly, if they are: State secrets privilege. Poof goes that problem.
The only real challenge would be a massive public uproar suitably close to an election that someone needs to be sacrificed, and how likely is that really? It's not a surprise that this is happening; the only surprise is that anything resembling proof has leaked. What are the odds that this will suddenly tip the balance and cause sufficient lasting outrage?