I have some experience in health, but not a lot, so take this with a grain of salt.
I've never heard of a true health organization (pharma, hospital, clinic, or lab) that used proprietary software that they did not develop in house. So if you break up relationships into these categories:
#1: proprietary, developed in-house
#2: proprietary, developed by a shop
#3: licensed third-party
...then I only know of the using #1 or #3.
If you're referring to public health or insurance companies, that's a different story. This company does exclusively the former: https://www.standardco.de/