Mate, I think we all know that there's more than one meaning to the term "public" (resp. "private"). What I wanted to emphasise is that there's a meaningful sense in which an internet forum which can be viewed and interacted with by anybody (by default) can be described as "public". Hence I argue that it would be beneficial for society that it be treated as something more than just the absolute domain of the operator of that website.
Reasonable people will certainly differ on this, but we're not arguing semantics, or about violating the sanctity of someone's control over their personal sphere.
How is this different than a large store like a supermarket where you buy food? The only difference I see is one of geographical barriers, and I don't see how that should fundamentally change the dynamics of how to appropriately deal with inappropriate or disruptive behavior.
Reasonable people will certainly differ on this, but we're not arguing semantics, or about violating the sanctity of someone's control over their personal sphere.