Jim, since no-one's ever managed to show that they're sensitive to Wi-Fi, why not ask the kid and her parents to help you with a simple experiment? Agree that you'll turn off the Wi-Fi, and then turn it on for one day at some random point. Then two weeks later (when the day has come and gone), ask the kid and parents to report back.
You could even join forces with the school science teachers and make it a science experiment by getting the entire school involved, with statistical samples from each class to check the possibility of age having an impact. Any decent science teacher should be able to work out some better scenarios than the one above - or even better, get the kids to figure some out.
Then the school can show that not only are they trying to do something about it, they're also trying to advance the state of medical science. Sadly the UK isn't much keen on children's involvement in experimental science, because they don't have science fairs like the US do, which is a real shame. Still, there are some UK awards for school science projects which are worth a look. And it'll get the school in the papers too.