> I know from experience that every hospital is different ... my gut tells me the application will actually need a local database in each center, within the hospital network, which periodically replicates up to central cloud database
What data are you trying to store? Pretty much every EMR/EHR system nowadays speaks HL7; if your goal is to integrate with those EMR systems, then your own application could circumvent a lot of issues by speaking HL7 as well. Of course, this only covers certain use cases, hence the question.
> their IT departments range from strict to extremely strict
Eeyup :)
> I am also aware of the HIPAA-compliant PAAS services out there and we may end up using one of those.
You definitely should. Else, be prepared to deploy your own physical servers and provide similar assurances of HIPAA/HITECH compliance. Hospitals already tend to be wary of anything pertaining to patient data living beyond their own networks.
> There's been a lot of talk about healthcare moving to the cloud
For some small clinics, yes, this is somewhat attractive. Once you move into medium and large healthcare organizations, hospitals, etc., however, the desire is almost universally for things to be as self-hosted as possible if they involve PII. Most EMR vendors prioritize local/onsite deployments IIRC (with one notable exception in my experience: CPSI, or "say-pay-ess-eye", as it's more commonly known).
> Am I right to assume that it's nearly impossible to set up a cloud database that is accessed directly from, say, the OR of a hospital?
Not impossible. Just excruciatingly difficult, with difficulty scaling exponentially with the size of the hospital. :)