They could be anywhere between no one but your doctors (and maybe your insurance company) knows anything and every single person alive knows all of your health records.
Showing the second case is easy: Build a blockchain for whatever purpose containing all health records of a country, a union, the world, whatever.
Showing the first case isn't much harder: Your doctor creates the health records + a long enough nonce and keeps them until the end of a constant period of time (e.g. til the end of the month), and hashes them + the nonce. They then send the hash to an authority which builds a blockchain from them for every doctor. In this case, no one even figures out whether you visited a doctor (Note that the data accumulated at the end of the month can be empty. In fact, it is likely to be empty for the majority of patients.) or which doctors you ever visited because of the blockchain.