Huh, I just learned something new. I have never heard anyone say that a professional "should" have FB, Twitter, and LI. Linked-In, I can understand.
My Facebook is account is strictly personal, and I have my privacy settings quite high simply because it's my personal page. I don't post anything that I would be ashamed for anyone else to know, but I do tend to post about my political, religious, and social beliefs.
I also do not list where I am employed or anything about my work life at all, because I don't entirely trust that my privacy settings are all they I may hope they are. Also, I have a blanket policy that I do not Facebook friend anyone that I work with. Since it has been recommended to have several social media forums, perhaps it would be best to have a strictly personal FB page, and then another one for your professional persona.
Take all of this with a grain of salt, though, because FaceBook tends to frustrate the daylights out of me sometimes.