Blockchain technology could indeed be the solution to questions about patient data safety and privacy.

For example, patients could be given the choice to decide what data to share (store) in a public ledger, and what to keep private.

I think the vast majority of patients won't have anything against sharing their crucial data or parts of their medical history if that's going to save their lives.

For example, every medical institution should have access to patients' blood type, just in case urgent blood transfusion is needed.

On the other hand, there are alwasy delicate data (e.g., AIDS) the patients could decide to keep private, not share at all, or possibly encrypt on the blockchain and share only with medical institutions of their choosing.