Health Records, at the local level, only really became more secure when IT based systems were introduced. Up to that time paper-based files could and did walk off in all directions. But off course with new technology, as I am sure we have all experienced, is the tendency to try and stretch it further. So these days specialists on call for emergency cases can see the readings, scans and notes of a patient before they leave their house to race to the hospital.
All the medicos I have spoken to in recent times (and that is quite a few) say this saves lives, because carefully considered treatments can begin before they arrive on scene. I have heard that a number of studies have already shown that this is the case.
However, with IT systems, remote access etc, there are risks of information being exposed to third parties. It comes down to the risk assessment, and that as things stand the proven benefits of remote access outweigh the risks of health data being accessed by unauthorised parties.
As others have said, the MyHealth record is a summary of treatments at the local level, whether in hospital or by GPs, or in specialists rooms. In this case the same claims are made, that having access to health records in an emergency where someone presents far away from home, will save lives and/or reduce harm. But I believe it will be some years down the track before the statistical records can confirm whether this is in fact the case. I opted-in to the "personally controlled electronic health record" or PCEHR some years ago before it became the opt-out MyHealth record.
BTW I'm about to follow you back to Mexico ( City). Gotta check out that mega temple 
