Facebook tried to get hospitals to share "anonymized data" on patients with it, including conditions and prescriptions, for a "research project."
While the data shared would obscure personally identifiable information, such as the patient's name, Facebook proposed using a common computer science technique called "hashing" to match individuals who existed in both sets. Facebook says the data would have been used only for research conducted by the medical community.
The project could have raised new concerns about the massive amount of data Facebook collects about its users, and how this data can be used in ways users never expected.
Emphasis mine, to make clear that the whole point is identifying individuals. Privacy laws prevent specifics being shared about patients, but anonymized data becomes onymous probability when compared to what's known. A broader, more long-term problem with Facebook is that what they don't already know about you can be bought from someone else.