The whole issue about the nurse answering the phone to begin with...
I picture her going about her job duties, filling out paperwork in charts, checking on patients, etc. The phone rang, she answered it, and being an honest person, wasn't prepared to be 'on guard' for a prank -- unlike a receptionist who normally may field such calls.
As for the hospital, I've worked night shifts at hospitals (not as a nurse), and it is very slow and quiet. I don't necessarily believe that the hospital was being cheap as much as it was being efficient. Imagine how much it would cost to have receptionists at all nurses stations through the slow hours when there may be only 1 or 2 calls, if any.
I also know from experience that unless you've seen firsthand public backlash about something you innocently said or did, many people don't anticipate that what they say or do may be used publicly against them. My first year teaching (before becoming a psychologist), I was young and naive. The school I was working at was new and had a lot of kinks to work out. A parent asked me my true opinion of the school, and - I gave it, privately. She then stood up at a PTA meeting and told everyone what I said. I could have died on the spot. I nearly lost my job but learned my lesson... I am not saying this nurse was naive as she had been on the job a few years, but I don't believe she anticipated being duped or the negative publicity - or gave a second thought to putting through a so-called family member to another nurse.
Nor do I think the DJ's meant any harm. People with thicker skin that are shock-jocks and such just may not realize how deeply their actions can affect others. It should not have been aired, IMO, but I really don't think they thought it through, as they never expected to get through.
It's a tragedy all around.