I think you are onto something. Social Media networks are themselves an extension of one's personality, just like one's membership in a church, professional organization, or any other group. As defined by Erica O'Grady, Social Media is not about the technology but about the relationships. Members of Congress have restrictions against use of government resources to promote their campaign or enrich themselves, such as use of a government office or computer. However, there have never been any rules to my knowledge against use of one's personal networks and personal relationships for legitimate purposes - you are going to communicate with people you know about any number of topics. One's connection to his/her twitter followers, as connected via a free, public domain is in and of itself a relationship. If you bar or restrict the use of twitter, you restrict the relationships, and that is a restriction on our Constitutional right to assembly freely.
Interesting Story: A father and son tour history and discover the future. My favorite moment has to be of Rep. John Culberson's Qik ambush of the TMZ cameraman.