Lets get something straight - most ten year olds when opening their mouths lie. The mother here, loves her daughter and accepts what she says is true...... but lets examine some facts
1. We are led to believe that a butter that wouldn't melt in your mouth sweet little girl went up to a bully, gently pushed him in the back to get him to go down the slide. He didn't go down the slide but instead got up and whacked her in the mouth.
This did not happen like this. What sweet innocent girl is going to do that to a boy with previous. It is much more likely that she is the bully and was picking on a timid victim! She wouldn't dare do that to a known bully.
2) If you are sitting on the slide with your legs down it and hanging on to the edge of the slide or the handles, facing down the slide and then get pushed in the back, how are you going to get any leverage to turn round, get up the slide and whack somebody in the face. As soon as you release your hands, you go down the slide. Therefore I don't believe the girl's story.
It is much more likely she picked on a weak kid and when he was pushed he tried to grab anything to stop himself going down and just flung out his hands and accidentally hit her in the face. He wouldn't have looked according to the asker he was on the slide facing the other way.
Don't believe your kids, they can be angels to you, but devils with other kids and they all lie!