True, this wasn't the most egregious. But the principle still applies. He said himself he held this back until his final check cleared.
A large company acting out spite towards a former employee has happened more than a couple times. Minimizing that risk seems entirely reasonable.
As others have said, I really don't see anything that's especially private in the article. The author wrote in pretty general terms.
I'm not personally aware of signing something that says "I'll keep all internal details private" though I agree I'd be highly unlikely to refer to anyone below the SVP level by name -- but I think that's exactly what OP did?