Back in the old days, public figures like actors and singers and other celebrities were often unreachable except through their publicist. Any time they were at a public event, there was their publicist, ready to stop any unflattering questions or to stop their client from saying anything they shouldn't say.
And then came Facebook and Twitter, where said celebrities can speak their heart's content, and dangerously, off the top of their head, without the filter or oversight of a publicity, and without the ability to withdraw what they wrote before the information is already spread around. I don't know that a publicist would really be able to tell their client not to use Facebook or Twitter, but then the publicist just might be in the position of doing damage control because of what their client says.
Celebrities on Facebook just have to be aware that what they're saying goes out to everyone. No tweeting when drunk, and seriously, think about what you're saying, at all times.
I ran across this article today that addresses the very topic of celebrities being able to have this direct communication with their fans and the rest of the world. I'm amused that what Demi Moore posted was used as an example. OK, so she pretty much said she was going to have sex with her husband. It's not like she was picking up some random guy off the street, and she's not exactly had the image of the pristine virgin. Having sex with your husband is not illegal or even particularly risque. Is it TMI to know they're having sex? I suppose it could be regarded as so. But it would be a much more damaging post from someone who wasn't married or someone who relied more on their wholesome image.
But I expect that the job of a publicist has gotten much more difficult and complicated in this increasing age of immediate and direct communication.