This is a story that I was told by a co-worker of mine a while back. To give some background on the issue: I also work at a hospital library that is also open to the general public and patients. The woman in this story comes in on a fairly regular basis and is known to get very moody and approaches library staff with some very strange requests - including this one.
One Saturday afternoon she came up to our reference librarian requesting that the librarian log on to her personal Facebook account to see if some man was "really dead". Apparently the man had blocked/deleted the patron from his Facebook for whatever reason and so she wanted to see the dates/times that he had last posted status updates because he, or someone else, claimed he had died recently (probably to get away from her). The librarian said that no, she could not do that, as it's a matter of privacy. (AKA: if you were meant to have access to information on his Facebook, you would still be on his friends list!)
The patron then proceeded to get very belligerent and told the librarian she "probably didn't know how to use Facebook anyway". She then went around and asked each of the circulation staff to log on to their Facebook accounts to spy on this man for her. None of them would do it for her either and she left very unimpressed.
I wonder if anyone else has had an experience with this issue in their own library? I can totally see creepy and "out there" people trying to use reference staff to spy on ex-partners and ex-friends.