Fair enough; we're using different definitions of "private." I'm using it in the legal/operational sense relevant to whether a government service was withdrawn

Fair enough; we're using different definitions of "private." I'm using it in the legal/operational sense relevant to whether a government service was withdrawn (agency vs company, public law vs company law). By that definition, it's a private company. You're using it in a shareholder-ownership sense. That's a valid perspective, but it's a different question than the one being discussed here.