The few times I have been in a hospital, I have not wanted visitors. I have wanted privacy (when I had babies and was trying to nurse), drugs and privacy (when I had surgery) and oxygen/breathing treatments (asthma). I didn't want my own religious leader visiting me, I didn't want a stranger visiting me and grilling me or my DH about whether we were his flavor of Christian. Hospitals are not there for that reason. They are there to help people in physical need. If one is in spiritual need, there are churches almost everywhere, they are pretty easy to find - most of them have big spires, bell towers, big crosses, etc. Of course the big sign on the front that says "Church" is often a good clue.
Nope, when I'm in the hospital, if you are not immediate family or caregiver, you probably might want to think twice about visiting and whether you will be welcome, after all I'm either in great discomfort, asleep, recovering, half-naked, half-coherent, not coherent, etc. My dad just was in to have his pacemaker adjusted and he was NOT himself. He had a bad reaction to the drugs and he was somewhat out of control, loud and yelling (he's 78, we forgave him and we knew it was the drugs). As a family we would not have wanted anyone else to have seen him like that. HE would have been totally mortified and embarrassed as he is very much old school gentlemanly.
I understand death watches, critical injury, things like terminal cancer. Totally different situation, then it would be acceptable for someone to ask the family member if they would mind if they could offer a prayer to ABC Deity in behalf of their relative. I am on the OP's bench on this one. This was way beyond rude.