While the CEO does not have to have experience in the industry, I do think that at least one member of the founding team does.
Healthcare is not a consumer industry - you can't expect to be successful with just a great product. You need to understand the complex politics that go on behind purchasing decisions as well as clinical end-user adoption (ie, physicians might love the app, but if nurses hate it, and *they* are the ones doing the data entry, your adoption and end results will still be poor). You need to have an appreciation for how to drive change management within a clinical setting, as well as user preferences.
More importantly, success metrics are much more important than with a consumer app. For consumers, "this helps me do X" is sufficient. For a hospital, often balancing on razor thin margins, with a hoard of report outs they need to do to various regulatory bodies you need to be very precise about the expected outcomes. While "a better patient experience" is noble, and no one will disagree, a hospital will not make a $200K purchase just to give patients the warm and fuzzies.
I see way too many "patient-provider communication" or "care coordination" apps and the like developed by teams of designers or engineers who think that all of the problems in healthcare boil down to just developing a prettier interface over the patient experience. While pretty is nice, effective is far more valued. And to know how to make an app or healthcare product effective requires some background in the care delivery sphere.