The paper linked in the Wikipedia citation for that line has the following in its abstract:

"The governance of central banks has two dimensions: corporate governance and public governance. Public governance is an institutional framework whereby the general public governs a central bank by and through the legislative and executive bodies in a country (...)".

"Independence of the central bank" means independence from direct intrusion by the executive branch, in the same sense the judiciary is independent from political interference.

So, generally, are courts, police and civil servants.

That doesn’t mean that those are not government institutions.

You used 'privately owned' to indicate it being shady.