I suppose if you have a drivers license + medicare card you could start applying for things like passports or loans. Perhaps you could get a license from someone by selling a second hand car and asking them to hand over a license while they take it for a test drive. It could also be used for blackmail I suppose if you've used a medicare for some sort of service that you want to keep private.

I think you're right though. All the people that make the most money from having health data could just lobby governments for access or just ask their customers for it.