Ultimately, it was the Royal Security/Hospital Security that was at fault. When a Royal visits any public place, I assume the RS must do a risk assessment and put in place the right security to fit the particular situation. In this case, the RS must have at least thought of the media phoning up trying to find out sensitive information. If this had been covered properly, prank calls would have been sweep up in the mix.
The female DJ has every right to be treated like her male counterpart. If you are put into a particular situation in the workplace, it's the employer that is required to look after H&S. if she feels she's been treated differently then it's quite within her right to challenge this.
The morals of pranks calls could quite easily be debated, but not simply as applied to to this one case. They would need to concidered as a whole as to whether they are socially acceptable. In fact, the Royals initially took it as the joke that it was intended with Prince Charles asking a reporter 'Do you think I'm a Radio Station' with a grin on his face when asked a particular question while boarding a boat.