For medical records - consider a secure reader tablet-like device. It has encrypted hardware which can be temporarily permissioned to have access to encrypted data based on blockchain timestamps. It is tamperproof - if you open it it has some self-destruct mechanism. Data is accessed in chunks, therefore the owner of the data can see whether data is being accessed in the way a human might use it, or if it is being downloaded en masse. The organisation with data access devices gets audited on an annual basis to see where all their access devices are and to ensure none of them are being tampered with.

Suddenly, we get to a situation where the security of the medical file begins to resemble that of the paper-based medical records department. If you want to copy records, you need to physically go to where they are, get access to each individual file, and go page-by-page photographing each.