If it's publicly available then it's public, otherwise it's just deep web requiring authentication which is not public by any means. WWW was designed to be public, if you don't believe me you could ask Tim and "World Wide Web Foundation, which seeks to ensure the web serves humanity by establishing it as a global public good and a basic right." (http://webfoundation.org/about/sir-tim-berners-lee/)

What Tim Berners-Lee aimed to do is largely irrelevant, it's how it works in practice that matters, and in real terms, it's not public space. You can be banned by the owner with no rationale, or access could be restricted behind a paywall with no notice, or content you contribute could be deleted with no notice.

The World Wide Web Foundation has no particular standing and no authority on what actually happens on the web.

Shitty metaphors are shitty. It doesn't detract from my point. I'd avoid using Google if I could, but they seem dedicated to interacting with me even when I go out of my way to avoid them. I'm not going to accept that I'm the bad guy when I try to fight back.