I'm not sure where you're drawing your implications from, but that is not implied, to me. I frequently see the concept of privacy applied to situations where an entity isn't required to ID themselves for the sake of privacy.

The common description when contrasting anonymity vs privacy is that anonymity allows one to do things publicly without being ID'd while privacy allows one to do things without the public having knowledge. There is no implication or requirement that the private party has been ID'd by another other entity.