If the agreement is as has been speculated, the press get access to images that are at times the press will be putting out stories about the family, but the images are controlled and not invasive.If like some suggest and the Royals have an agreement with the British press/media not to print pap pics, why not? I can understand not having pics of the kids printed in the papers etc but what's the issue with a pap pic of say Kate going to Waitrose?
Given that Kate went through having topless pictures of her taken via long lens camera in a space she had an expectation of privacy, it's unlikely she has much trust the paparazzi will respect the personal space or boundaries of herself or her children without having their access to pictures at times stories are expected being held over their heads.
There's also nothing to gain from paparazzi images of them save for a couple of minutes of entertainment for bored members of the public. Someone being famous doesn't make their supermarket shopping any less tedious than anyone else, so I can't imagine a good reason to violate someone's privacy for tabloid fodder.