Correct me if I'm wrong here, I thought networks, especially news networks all have a 30 second lag time in their broadcasting to edit out material they don't agree with or may get into trouble for?
If so, FOX could'a edited out that "offensive comment" and kept it out of their broadcast. Ergo, it seems to me they intentionally wanted to get that part of the message out there and then provide cover for themselves by "apologizing" after the fact when they could have done something about it during the broadcast.