That’s a distinction without a difference. He was directly CIA for a bit, and went through the revolving door to a contractor who was placed at the NSA. It really doesn’t matter which corporate entity’s name is on the pay stub; it’s all the same public-private scam. Whether or not Booz gets a percentage of the tax money firehose for running the payroll or not is of no import.
All of this is covered in his book, which is a decent read. I recommend it because it’s information dense and quick.
Furthermore, I said he was deep into the NSA (which he was), not that he was employed by them.