Plenty of people had “private” LiveJournal accounts back in the day with no expectation that it was a zero-knowledge system. Just that they weren’t sharing it. I may not be a good indication of “most people”, but I just don’t think that most people think of privacy in the way that we (folks who know details of encryption and metadata leaks) do.
I disagree. I believe that it’s more common for “private” to mean “between you and the company”. Eg. Private accounts on other services, or private information associated with your account.