Yes, not everybody does that and not everybody does that to the fullest extent, but it's the same ideology just applied to every last facet of interaction.
Of course this isn't how the web started. The Internet was built on military technology and first settled by scientists, amateurs and aspiring tech nerds. Everything was free because it seemed obvious that "information wants to be free", which really just meant charging for bytes more than it cost to generate, store and transfer them (i.e. deriving "surplus value" or "profit" if you want) seemed like a rip-off even when commercial BBSes started popping up. If you wanted to put an edge on it, you could even call the early web a form of "primitive communism".
But there's no reason to bring politics into discussions of technology of course. Running websites costs money and how else are people supposed to turn a profit on providing a service if we don't find better ways for them to charge visitors for access?