Not telling CASA Avmed is not the same as not obtaining proper and successful medical care. As the Abstract of the study notes above, plenty of pilots seek what the study calls "informal medical care".
The laws of physics mean that there is no causal connection between Avmed's levels of knowledge or ignorance of a person's medical history and that person's level of medical fitness. A person's level of medical fitness is what it is.
There are plenty of pilots out there who are not obliged to tell Avmed anything and about whom Avmed knows nothing, and those pilots meet the aviation medical standards. They just don't have a piece of squashed tree from Avmed saying so.
(Note: I am not advocating that people should withhold information from Avmed.)