As someone with access to data on 50 million patients and having studied aggregation of medical data for last 5 years I can assure you that its not easy as it sounds.

The amount of noise that "theoretically guarantees" privacy protection in terms of epsilon renders any reasonable analysis impossible. E.g. How about CDC telling you that there are 0 - 2000 cases of Ebola in Massachusetts.

There are theoretical guarantees provided by Differential privacy and then there are actual requirements of conducting public health or biostatistical reaseach with certain evidence value. The gap between the noise added by the former and tolerated by the latter is enormous.