That is not true.
This is utter tosh.
C'mon.
I'm not getting into a public/private thing, but I know for a fact that this still happens. Fair enough, it's certainly much less common than it was (thankfully) but it's still not exactly rare.
I know a locally based public sector section manager who is barely literate, and presides over 3rd level educated staff, has zero management skills, zero HR skills, but he has been there "a long time".
Some of my inlaws work in the civil and public sectors - this culture still very much exists. In fairness maybe I am experiencing the last of the old school before they retire - I hope so.