When everyone is unique there is no such thing as anonymised data
If you wanted to find Stephen Hawking's medical records all you would need is his date of birth and the fact that he had amyotrophic lateral sclerosis (ALS) a form of motor neuron disease.
People with this disease do not normally live as long as Stephen did so there would be very few records with a similar date of birth. If it was known that he had certain complications at certain times, this would narrow down the choice considerably.
Leave out this information and it destroys the usefulness of the record.
You don't need much medical information to identify a person, considering everyone is unique.
And if someone has few or no medical problems they may well not be be in the database.