"Public company" is a very specific thing; the BVG is state owned, but very much not a public company.
Would you consider In-Q-Tel - wholly owned by the CIA - to be a public venture* through ownership by a government agency, or a private one, because the public has no opportunity of ownership or control? I'm convinced it's the latter.
* Let's ignore it's non-profit status. Any CIA shell-/front-company is an even better example