IMO, those arguments are grasping for specific definitions of 'ownership'. In its essence, the non-profit structure represents the concept of 'public ownership' to the fullest extent possible under the law. Of course, it's missing some characteristics typically associated with private ownership but it has the core component which is "It should serve the public" which mirrors the idea that a corporation should "Serve its shareholders."

I think if the non-profit retained over 50% of the shares of the for-profit subsidiary, a case could have been made that the public-benefit aspect is still dominant. But with only a 26% stake, that argument cannot be made.