Could passengers on an airline flight create an out-of-CG situation by moving around the airplane?
I was on a flight in an SWA B737 that was mostly empty and the flight attendants moved us all toward the front. They told us it was for balance reasons. 

I don't think this was a factor on flight 93. The CVR recorded the hijackers discussing what to do about the passengers. The hijacker piloting the plane asked 'Is that it? Shall we finish it off?' Another hijacker responded, 'No. Not yet. When they all come, we finish it off.' Then a few seconds later when it sounds as if the passengers are getting through the cockpit door he asks, "Is that it? I mean, shall we put it down?" The other responded, "Yes, put it in it, and pull it down." That's somewhat odd phrasing but those are translations from Arabic. It's clear that it was intentional.