Consider the following de-identified data sets:
- [date, time, clinic, procedure or test being done, insurer] - as collected by the clinic chain so that it can get money from insurers
- [month, clinic, test name, test result] - for all tests made in the last year, collected for statistical purposes
- [date, time, latitude, longitude, phone number] - because AFAIR telcos sell this data
- [name, surname, phone number, ...] - some insurance company's list of customers
If you can get your hands on these datasets, you can trivially de-identify patients and even assign test results to them with high probability (that depends on how many tests of a given type are made in any given clinic per the unit of time used to group the second data set).
Real-world data sets may be less clear-cut than this, but there is more of it, and you can apply statistical methods to find correlations. You don't need to be 100% sure customer X has diabetes for the information to be useful to you; 70% or 60% is useful too.