I've brought up this concern several times. Having worked in a hospital for almost 16 years, I realized that in the demographic information that is collected, often one of the entries is to specify the patient's religion. Once that detail is in the patient's record, individuals who are cleared by the hospital's Pastoral Care Team may have access to the list of patients who are affiliated with their religion.
So, for example, as it happened to me, I specifically signed a document (while I was still a JW) that I was not in need of a visit from the Pastoral Care Team, who happened to be an Elder™ in the local Congregation™. In any case, the Elder™ showed up while I was behind a privacy curtain breastfeeding my newborn daughter, and he waltzed right in to greet me. I didn't know him from a hole in the ground, being from a different Congregation™ and Circuit™, and I sure wasn't impressed that he invaded my privacy the way he did, especially since I'd declined in writing any visits from the Pastoral Care team. I asked him how he learned of my presence in the hospital, and he informed me that he was given a list of all JWs in the hospital and my name and room number were on that list. I asked him if he was aware that I had declined a visit, and he said that he was, but he just wanted to make sure that I was all right, and whether he could bring me the Magazines™ or patch me in on the phone line for the Meeting™. I showed him that I did, indeed, have the current Magazines™, and that I declined the visit because I had Friends™ and family members visiting me, and that I felt that his time would be better spent looking after someone who was truly alone and needed the company, and I was being discharged home in the morning.
I can only imagine how someone would feel completely ambushed if they had accepted a transfusion and then have someone like this show up to their room, uninvited, while the infusion was running.
My advice, as an insider, to anyone who is going to hospital for surgery or in anticipation of unforeseen events (like an accident): please go to the hospital's Admitting Department and specifically request to have that little "JW" in your patient demographics REMOVED. This is how the HLC will find you if you are known in the hospital records to be a JW. If you don't want an ambush type visit, take care of it ASAP.