Your statement is patently false. That one investment would need to run into the hundreds of millions of dollars, perhaps even billions, to produce every piece of software for which no Linux option exists... PACS software, laboratory information systems, radiology information systems, clinical portals, clinical coding applications, MRI controller software, linear accelerator controller software, haematology analyser interface software, EMR software, patient administration systems, and THAT's just for healthcare! Imagine the rest! On top of that, building all this software would take at least a decade.
So no, they can't switch to Linux and open source freely. In fact, it'd be bloody expensive and an incredibly long process - that would divert billions of dollars away from front-line operations (and stuff like pharmaceuticals etc) for no good reason.