Sort of.
The military is not a homogenous organization. Q clearance specifically points to DoE, which is nuclear weapons.
There are things which have been created and classified, divested and misfiled, forgotten about within the burauecracy of our government and which grow and take on independent life outside of it.
Have you heard of the GrayFish Malware?
No Such Agency.
That isn't the NSA. The NSA is just as competent as the DC police. As is the strategic and operational command of our military.