I think you're thinking about it more from the technical persons view of privacy. Most non tech people do not think about these kinds of privacy concerns or worry about what Facebook knows about them. They already have likely shared a ton of data with Facebook and don't care and likely don't care to share more. However they may be concerned if they found out every business they go to was getting a bunch of personal information about them.
So I think the general consumer would be more concerned about all these random places they go knowing who they are and details about them. This is what I believe Facebook is trying to state, that no business gets any of your information. Not that Facebook doesn't get anything. So yes they poorly worded what exactly is private and what isn't.
Do you think the average non-technical person interprets "designed for privacy" as "Facebook gets information about all your movements"? I wouldn't think so personally.
So I think the general consumer would be more concerned about all these random places they go knowing who they are and details about them. This is what I believe Facebook is trying to state, that no business gets any of your information. Not that Facebook doesn't get anything. So yes they poorly worded what exactly is private and what isn't.