Regarding Remedy's missed flight to CMH because the door closed just before Remedy got there from a connecting flight, what is the policy on re-opening boarding doors once they're closed? Is it an airline policy, or up to each GA, or an FAA rule?

I've seen people get turned away before for NW flights when the plane is still at the gate for several more minutes, but last night I was on a Southwest flight from MDW to DTW, the boarding door had been closed, and about a minute later we were still sitting at the gate and there was a knock on the boarding door. An FA opened the door, a late connecting passenger got on, and then the FA closed the door again. We pushed back about a minute after that.