For the record, I'm working on a topological data analysis project that is in some ways quite similar to this, and I'd be astonished if a single community hospital has the depth needed. We're working with thirty-some.
The key here is that TDA is packaged into an application that is designed explicitly for use by practitioners. All of the underlying math (and you know there is lots of it in TDA) is abstracted. What is shown is the groups and the atomic level explains (this group is here for these reasons e.g. they received albuterol upon admittance). Your instinct is correct, but that is what is interesting about this case - the hospital, without a single data scientist, was able to to achieve this with only slick SQL skills and engaged doctors.
Screenshots for the app and videos can be found here: https://www.ayasdi.com/solutions/clinical-variation-manageme...