The issue with such highly sensitive data is that it's just data. Probably a few GB. Many AAA game downloads nowadays are much bigger than that. Even if they protected their database (article says they didn't), it's easy to break into a place that has all the data collected compared to collecting it yourself from doctors all over the country. There's an easy solution to this: don't concentrate highly sensitive data.

With nuclear material, the IAEA has set up a sophisticated surveillance regime to make sure that countries use nuclear technology for peaceful purposes. Everything that contains nuclear material is video surveilled. They collect probes and check composition to prevent someone taking, say 1%, replacing it with filler material, and then mixing it again.

If we concentrate data, we should employ such surveillance regimes for highly enriched sensitive data as well.