From the story …

Members of the party, all but one of them U.S.-born citizens who were headed to a religious retreat in Florida, were subsequently cleared for travel by FBI agents who characterized the incident as a misunderstanding, an airport official said. But the passengers said AirTran refused to rebook them, and they had to pay for seats on another carrier secured with help from the FBI.

So it was a retreat and not a conference. My bad.