It really is up to you. Many parents find it helpful to have a diagnosis to keep the child gluten-free. Apparently schools often respond better to a diagnosis rather than just a parent's word about the matter. I haven't had that experience but I am in Canada so perhaps it is different (my kids are gluten-free without a diagnosis).
There are some around here who had a positive biopsy with negative tests but there are not too many... It can happen.