The callers thought that they were being ridiculous - they thought that their accents and use of language and so on were so obviously daft that they had no idea they would actually get as far as they did. They thoguht they'd call, say some silly things, and have people laugh at them for being so inept at impersonating royalty.
Tragically, working for the modern NHS is for many people a stressful unpleasant experience with a lot of management and bureaucracy.
I note this is the station that had a massive boycott due to one announcers finally going too far. You might want to look up "Sack Vile Kyle". [1]
There is no doubt that 2DayFM we're hoping for massive shock and outrage. That is their modes operandi.
1. http://sackvilekyle.blogspot.com.au/2012/03/vile-kyle-bad-be...
To change from my original tone a bit, perhaps it is best to generalize the idea, that having fun at a stranger's confusion, behind the anonymity of a phone, is just too cruel and dangerous. You can't know what's going on in the lives of the people you call, and the consequences move out of your control when you hang up.
The fallout here in Australia was utterly predictable; contrite and teary disc jockeys, people baying for their blood, current affairs shows doing segments left, right, and center. Equally predictably, the hospital was trying to shift responsibility for improperly managing patient privacy.
The annoying thing is that it took someone's death to show just how humiliating and terrifying being on the receiving end of these things is.
On related notes, it's interesting that the author of OP says, "Just last summer, someone called me and claimed to be holding my brother at gunpoint. The ringing of my phone startled me for days to come." She also regrets making a mean-spirited call to her math teacher. Yet she does not seem to regret prank-calling in general.