Well if a billionaire controls a public square, I wouldn't consider it a public square.

Edit: one thing that bothers me about HN is the context-less downvoting. I wish people would reply with why they're downvoting. For me, it wouldn't be a public square because it is privately owned, it would be more like a shopping mall or an amusement park. Just because a shopping mall has free admission to the public doesn't mean it is a public space.