False it cover much more than that and the claim is that the "private entity" would be going public, so yes you would be "registering" such sales or offerings:
Last I checked taking a private company public means you intend to register shares for public use. Is that not what an IPO is all about? The point is clear there exists no exemption in which a private subsidiary can issue or sell shares to anyone outside or external of the company unless they qualify for an exemption or are part of the funding agreements. Shareholders of a public company cannot be given shares in the private company due to their public holding status in the parent company.