Another piece of information that I think is important is that she was an immigrant who was probably very committed to living her life well in England. Like others have noted, there's an allegiance to the royalty in England that we can't quite imagine here in America.
I also guess she didn't pick up on the accent that the DJs thought would give them away because English is her second language.
My guess is immigrants feel that allegiance to the crown even more forcefully than your average English guy, and that she would have taken this prank harder than your average English guy.
Of course, the leap to suicide can only be taken my somebody who is already seriously mentally ill.
To those who think the DJs are not in the least culpable for this, I agree that if the nurse was driven to suicide over this prank she was probably a ticking time bomb. At the same time, where there is life, there is hope. There was hope that she could have overcome her demons.
While I don't think the DJs should be punished or anything, it is an undeniable fact that as a result of their actions, that life and that hope was extinguished. They couldn't have known this was going to happen, but it did.
I'm throwing rocks out a window for fun. Just to try to hit a particular spot on a nearby tree. One time, a bird flies by and I accidentally nail the bird. Could I have reasonably foreseen this? No, of course not! But do I still bear some responsibility? Of course!