All it will take is one ATSB documented aviation medically related RPT incident and the General Public will demand that CASA Avmed be given access to E Health records of pilots. The Government will comply in seconds - for “safety” you know.
The trawling by Avmed will start immediately and what a rich haul they will find. Believe it or not, some Doctors are incompetent ratbags. There is no telling what irrelevant garbage is in your medical records right now.
For example, google Avmed and cancer. See what can be demanded of you, ladies, if you are unlucky enough to have been stricken with breast cancer, even if you are now totally clear.
My wife asked me about learning to fly last week. She has had cancer. I told her not to bother. The ongoing medical tests required by Avmed would probably cost more than the training.