They want to live tough, callous and venomous. But every once in a while they get nailed for going too far. That is troublesome. They actually fear for a moment that they won't be able to keep their position if they don't retract. The thought of losing their job is what brings them to tears.
It's her TANG moment. She must renounce her hateful conclusion or risk joining Dan Rather as a journalistic has been. Tears appear quickly at that thought.