Even which doctor someone visited is confidential data one ideally would not preserve when not needed anymore (and "ideally" might very well be law). Health data is messy, and I have trouble imagining a solution that puts it on a blockchain but allows only private access to everything and has a chance of fixing instances of leaked credentials while still getting value from the fact that there is a blockchain. (If there is prior work on this that actually goes into detail I'd be happy about pointers - sadly a lot of this stuff seems to end at the stage of whitepapers when it comes to public information)