No, it's a more fundamental disagreement than what constitutes a public vs private space, it's a disagreement about who gets to choose. If a private corporation gets to decide by virtue of ownership - property rights granted by societal contract to begin with - then they have unilateral, unaccountable power over society. We are in the process of deciding the nature of corporate personhood and how applicable the Bill of Rights is to organizations so what is "public" and "private" is still an open question.