Telling her she overreacted isn't going to help. It could easily make matters worse.
Don't we say here that you are entitled to feel what you feel when someone does something that bothers/hurts you?
Telling her she overreacted is adding yet another criticism. First, she made a mistake and she probably feels pretty stupid about that. Then a peer comments on it--more feeling stupid. Then the group leader tells her to shut up. More embarrassment and shame. Then another adult comes along and tells her she is overreacting--telling her that even her feelings are wrong. Trust me, that is not going to help. Been there, got the "you are just too sensitive" lecture a million times.
What I wanted to yell at all those people telling me I was too sensitive was, "You are just not sensitive enough! Why do you get to determine how sensitive I can be?" but I never dared.
If anything is said to the young lady, it should be along the lines of, "I could tell you were very upset by what happened that evening. Anyone would be embarrassed about making that mistake, and the comments people were making didn't help that any, did it? I'm sorry all that left you crying in the bathroom. I think there are some things you and I can work on that will help you to deal better when you are publicly embarrassed or criticized like that, so you can stand up to those people and not have to leave the group. Would you like that?"
Don't tell her what she felt was wrong. It wasn't. Do teach her how to handle her emotions better. Do teach her how to come up with a witty comeback when a peer teases her. Do give her the skills to cope with her sensitive nature so that she can get along with others with the least amount of hurt.
My parents told me for years that I was "too sensitive" when I reacted to the teasing my brothers subjected me to. Didn't matter if I ran away from them, cried, hid in my room, yelled, hit them--it was all my fault because I was "too sensitive." Decades later, several relatives have told me that they were very concerned when I was a child, because they felt my brothers were too aggressive, too bullying, allowed by my parents to take the teasing well beyond the limit of "fun." But in my family and in those days, you simply didn't comment on the parenting of others.
So I'm always very wary of the "she's too sensitive" comment. All too often, it comes from someone who has crossed the line but is unwilling to admit it.