Well of course it was the media who started it.. and it was ALL the media. And what I mean by that is, there is only SO much space on a magazine cover.. so they used "Princess Diana" and everyone knew who they were talking about.
It would have become quite difficult to always use "HRH The Princess of Wales", or "The Princess of Wales" on those covers.
Once they used "Princess Diana", it caught on and everyone began using the moniker to refer to her.
They've done the same thing with other wives of heirs..
HRH The Crown Princess of Denmark is commonly called "Princess Mary"
HRH The Princess of Asturias is commonly called "Princess Letizia"
HRH Maxima, Princess of the Netherlands, is commonly called "Princess Maxima".. etc, etc.
Besides, I don't consider it a terrible breach to call the wives of heirs "Princess", since for all intents and purposes they are intended to be future Queens.. unless, of course, they divorce the heir.
After Diana's divorce, the media most simply used "Diana", but by then she was a household name. Practically everyone on the planet knew who she was, and the media could sell their newspapers or magazines on the strength of her first name alone.
If Camilla had used her official title, HRH The Princess of Wales, after her marriage to Charles, I'm sure you'd now see her being referred to as "Princess Camilla" in the press. But since she uses the title HRH The Duchess of Cornwall, she is commonly just called Camilla by the media. I have never seen her called "Duchess Camilla" either.
It's an easy transition to call someone "Princess" when that is part of their official title.. and although legally Camilla is The Princess of Wales, since she doesn't use the title, its a little more difficult and/or awkward to call her "Princess" in the media.