[BjoernKW]

The same kind of system could be implemented with a distributed or federated EMR.

The data would still be stored with the practitioner where it originated but it could be shared with third parties (i.e. other practitioners) if the patient consents.

I really don't see how using the patient as messenger for medical data on paper could be seen as a privacy feature. Quite to the contrary, actually: Paper documents are easily misplaced or lost and then suddenly someone has access to your medical data.