Again I say:

Are we really supposed to believe that the royal family had not implemented some form of security for communication between the palace and the hospital?

This is the hospital used by the royals and surely they must have either a direct line (think: Batman's special red phone line) or some type of code system in place that allows the hospital to verify their identity.

If they did not, that means that anyone could call the hospital and claim to be any member of the royal family, which is outrageous, given all the ultra-security measures in place to protect them in everything they do. So if they want privacy and protection, it is incumbent upon the royals and their security team to implement such; if they don't, then they have to take into account that some people will likely try to get information, such as the prying media (or stupid DJ prank calls).

The nurse who died only took the call and put it through to the attending nurse who actually verbally provided the information to the DJs.

So the nurse who died apparently did NOTHING other than transfer a call.

Is that something that would cause a sane person to commit suicide? Imo, NO.

The hospital says they did not reprimand her and her co-workers were supporting her; even the royals claim they made no formal complaint.

So what about this innocuous incident would drive the mother of two children to kill herself?

There must be more to the story.

Either she was already terribly mentally unstable or someone was involved in her death.

Has it even been determined for certain that it was suicide?

Has it been determined where her husband and children were at the time of her death?