I'm a nurse and I can tell you that it is Standard Practice for hospitals to require ALL employees to sign a specific Confidentiality Clause at the time of hire.
The instances that Mad Apostate makes reference to appear to have originated with someone working right in a Medical Records Department.
Hospitals often offer patients the option of disclosing what religion they practice. The intended purpose of this information is so that Doctors and Nurses have some idea of the cultural practices and values that their patients hold (for instance, strict Jewish and Muslim patients do not permit autopsies, certain groups have customs related to birth and death, and we want to respect those values of our patients.) However, in the case of JWs, as you point out, this information can be abused by unscrupulous individuals. The best advice I can offer, if you are about to be admitted to hospital, is this: Do NOT, under any circumstances, disclose an affiliation with Jehovah's Witnesses. Once this information is typed into the computer, people who have access to the system can very easily determine how many JW patients have been treated, what treatments they received and so on. If you DO NOT DISCLOSE an affiliation, your name will not come up under a specific search for JW patients. It's imperative that your physician is aware of these wishes also, as they may in discussion with nursing staff who are caring for you mention in passing that 'he is a Jehovah's Witness', and that information may get passed into the system inadvertently.
Love, Scully
It is not persecution for an informed person to expose a certain religion as being false. - WT 11/15/63