I think they want to be left alone by the Windsors and the British press, not necessarily the media in general.
Whether they truly wanted absolute privacy or not, they're never going to get it. Once a monarch.... you don't get to just disappear and you're always a security risk (both ways) whether you've lost your title or not.
Who do we think keeps leaking things about them to the press that require some sort of response to prevent them then becoming the target of an enraged mob? And why can't the British rags find another story? Why do they have to go with what the Windsors are leaking every freaking time?