I think, @RecoIIectionsMayVary, it relates to them wanting to have more control over what the media can report. It links in with Harry's pronouncements on the First Amendment in the US.
It seems to me that some celebrities see media organisations as an extension of their own PR organisations, and feel they should be able to approve stories before publication. Much of what has been suggested as 'illegal' so far in this case has simply been unpleasant or upsetting.
That doesn't mean I would like it if I were on the front page in the same way - I would hate it. I do think though, there are things celebrities can do if they don't like the headlines (by which I mean take more care with their own information and social circle), and I think having a free press overrides discomfort, especially in the week a British citizen has been jailed in China for 20 years.