Re: Fax
That still does not demonstrate that fax transmissions are safer.
1 - TRANSMISSION over email is 95% encrypted. In other words, hard to intercept. What you're talking about is shared access, which is the equivalent of having a central fax machine at a hospital division's reception desk.
2 - At least there is at least still a layer of credentials in the way of access. A fax machine will spit out a fax when it receives it (most people do not even know about secure storage), whereas with an email there is at least some access control.
Maybe it's time to stop flogging. Your horse is really very much dead.