No, that was an example, not a requirement. Google has this history they associate whether or not you have a Google account. The account just solidifies it. You're still being tracked and identified without the account.
and that's an assumption you make that requires evidence. Your claim is that there is not only this kind of identification happening, but that it happens even if I have the common tracking blockers. Otherwise the blocklist in this thread would be completely overkill, just as I said.