How so?
Data transfer (i.e. lab results, consultation results) happens mostly on paper, that is the patient usually gets handed a letter with the results to present to their GP.
Lots of information is lost this way. Examinations and analyses often are duplicated or done repeatedly.
Which is also a privacy feature. Your dentist has your records, if a body is found and they think it might be you, they will ask your dentist for the records. If the mandatory storage period has passed, they are gone. To steal the records, an attacker would have to know, who your dentist is and then get them from there.
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.
With the current system on the other hand I have very limited control over my medical data, if at all.
Sure, when receiving results on paper I could throw away anything I "don't like".
However, I have no control over what records my GP, a hospital, or my health insurance provider keep about me. I can't see them. I can't have them amended or deleted.
Every time my local medical cartel upgrades their EMR, my personal history gets amended to include false information that could have impacts on my career, and lead a provider to make a bad decision.
It's the same with other medical imaging procedures. They have machines literally costing millions but they can't afford to have a secure system for keeping and exchanging medical data.
Up until a few years ago (according to my knowledge, perhaps this is still happening) paramedics routinely used WhatsApp for sending information to A&E while en route because there simply is no proper system in place to do so.
There is a system in place that tracks and records some things, like days off prescribed by base doctors, prescriptions for which national care pays and few other stuff, but most of everything else, including charts from when you are admitted in most hospitals and of course whatever you do outside of the public care (which kind of sucks and has insane waiting times, which means you most often do) is not included in that.
So.. nope.
You should see what it's like in the US.
Italy's certainly not perfect, but faults and all, I'd happily go back to that system from the one we have here in the US.
It does make a difference where you are in both countries, though; in Italy I lived in Padova, where things mostly work pretty well.