The way the public servants work is that they must be seen to be doing things that leave no stone unturned, as if they don't consider and mitigate all options, they can be in a world of legal hurt.
If there is an avenue for AVMED to access My Health Data, and they do not, should there ever be an accident in which the coroner discovers that the pilot has a My Health record of relevance to the accident, and CASA did not consider that record in the granting of the medical, then some AVMED/CASA folk will have a lot of explaining before the inquiry. I can't see AVMED ignoring My Health data, unless it is illegal for them to do so (but then a quick rewrite of the rules deep in an election campaign and pushed through as part of other legislation might see them access it in the future anyway).