I was just disputing the claim that 'privatization' connotes using non-government contractors, as opposed to specifically for-profit enterprise.

Whether non-profit private entities have the same properties that - in the case of for-profit enterprise - motivate critics of privatization to oppose government reliance on them, is orthogonal to that point. But on the subject, that might be true, but my take is that the important part to most critics of privatization is the entities are motivated by profit.