NOT knowingly /Unknowingly/NOT Wittingly

I am reading an article about Clapper saying “not wittingly” about N.S.A.’scollecting data on Americans.

https://www.newyorker.com/news/daily-comment/unwinding-unwitting

In the beginning, the writer writes:
“A truly straightforward lie would have stopped at “No, sir.” But, by adding a caveat, Clapper was signalling thathis “No” stopped short of being wholly the opposite of “Yes.”
And then there was this: he didn’t say “unknowingly” or “not knowingly.” And he didn’t say “unwittingly.” He said “not wittingly.”……”
In the end, the writer analyzes why:

“Just this: at the N.S.A., the staff members who knew the secret were known to one another as “witting” or “witty.” Those who’d been kept in the dark (me, for example) were known, though of course not to ourselves, as “not witting” or “not witty.”
Maybe I’m wrong, but here’s my guess: Clapper instantly knew that he’d made a serious mistake when he said “No.” He groped for some way to mitigate it, and what hefound, an instant later, was an intelligence-community term of art, a bit oftradecraft jargon having to do with the difference between the on purpose and the incidental, the guilty and the not guilty: witting and not witting, witty and not witty. Wittingly and not wittingly.”

After I read the article, I still
don’t understand the writer's opinion on the differences between unknowingly, not knowingly, unwittingly and not wittingly here?

Could you explain ?