When I was little I had the same problem, and actually still do to this day. I would complain that I had pain when I had to urinate. My mother took me to several doctors and also to the hospital for tests, nothing ever came up wrong, and then one day a doctor told my mom that my problem is stress related. Whenever I am especially stressed, it hurts to urinate. I still react this way but only when I am extremely stressed such as a job change or when I found out I was pregnant. It doesn't even have to be bad stress it can be good. When I was young it would be going to my grandmother's house, her and my grandfather argued all of the time and so everytime I had to go over there I would start having trouble urinating.
This could be your daughter's problem as well. Please don't be to hard on her when she says that she has this problem, because it really does hurt, just like a UTI. The one thing that I found helped me when I have this problem, is to draw a warm bath and relax in the warm water for a little while. I would definately say that the child at school is really bothering her, she probably doesn't want to let you know how much.