Well, what caused Edith to cross the street without looking both ways before Kirk got there? In the episode, she was compelled to get to the bottom of the mystery of these weird guys and find out how Kirk and McCoy knew each other. She was supposed to die in some sort of traffic accident, so what originally caused it?
One possibility: in the reality before McCoy arrived, the bum who got fritzed by the phaser was originally the catalyst. He was in that sport, possibly drunk and stumbling in the street in the path of the truck. Nobody else made a move to save him except Edith. She failed, sadly and they were both killed by the truck with bad breaks. This would then remove the bum from the timeline.