I'd call it a non-public corporation. A public corporation is one who's ownership is distributed among the public. The public does not have distributed ownership, as ownership would imply control. The public so-called=ownership has ZERO control over the corporation as a private entity has ALL control. As such, facebook is not a public company by the common meaning.

It is a public company in label only. This is a psuedo-public company as long as a single individual owns/controls the company.