From the website:
The patient must be informed about the information to be included in the directory, and to whom the information may be released, and must have the opportunity to restrict the information or to whom it is disclosed, or opt out of being included in the directory. The patient may be informed, and make his or her preferences known, orally or in writing.
At the hospital in which I work, we have a specific form-the HIPPA form in which people have to be specifically listed- by name and with phone number, in order for us to tell them what room a patient is located in and then an additional list if it is okay to update them on patient status. I would argue by saying no to a visit, and then having them show up-they are still in violation.
BUT, regardless of whether or not the legalities of HIPPA are violated or not, the mere implication of a violation is usually enough to make a hospital bend over backwards to meet your needs, because the fines for a violation are so large and the hospital should know that the court of public opinion is more damaging to them then even an actual violation would be. Usually they want to err on the side of caution, at least in my experience.
Also, depending on the size of the hospital, the chaplins who are there getting paid are most likely not denomination specific. If I am correct on the original interpretation I had, the people who visited were NOT hospital employees, but outside mormons "volunteering" to administer to the sick. I know in UT they have people on service missions for the specific purpose of visiting those in the hospital, but there is a much larger population there also.
It just really irks me that they can insert themselves where they were not asked or invited to come, and I feel the same way about all religions who prey on those in a compromised position while in the hospital.