You need to think of medical privacy the way you think of browser fingerprinting; it's not necessarily any single piece of information that lets you be tracked,

You need to think of medical privacy the way you think of browser fingerprinting; it's not necessarily any single piece of information that lets you be tracked, but rather the combination of a bunch of them -- even when "anonymized" -- adds up to enough bits to pin a consistent identity on the people involved. And given what the adtech space has been able to figure out pretty easily in terms of tracking even people who take serious steps to avoid it, you should not think that there is any reasonable amount of "anonymization" that can make otherwise-useful medical details safe to release.