To me the root of the RPS issue lies in our beliefs about whether a) we have the right to write about real people as characters in our stories and b) whether they or their families would be offended or object or be upset about them.
With regard to a), it is clear that the law leans strongly against us, the tests El Wing mentions notwithstanding. If someone writes a story that claims something that did not happen, the law states that this is a form of defamation. The fact that the prima facie case for defamation is so easy to make, and that it can cause harm whether we wish that harm or not (claiming a homosexual relationship between two known people when one of them is happily married to someone else can cause mental distress, for example). Whether the harm could be proven, whether anyone makes these claims in court or goes to the bother, does not address the prima facie case of defamation. Why would we want to write something that nominally fits the description of invasion of privacy, or of defamation of character?
b) I was told in private by someone who is friends with an actor about whom RPS stories were written. That person saw and read some of the RPS and, being a friend of the actor, was mortified and outraged, and told the actor, who was upset, not only about the fact that the stories were being published on the Internet, but that it was causing pain and anguish to his friends.
To me these are the core issues around RPS. It is not a question of author's rights. Clearly, if people have been writing about N'Sync all of these years and no one has been sued, then the risk of lawsuit may be small. But that, to me, isn't the point. To me the point is one of respect for the individual.