What are the credentials of the professional making the request on behalf of the child? Do the credentials verify that this person has the professional education, knowledge and experience necessary to legitimately make a diagnosis and recommend a course of action?
If the rcommendations are coming from an optholomogist or optometrist who is licensed in your state, you may not have a choice. If they are coming from a technician, assistant or parent, I believe your district can require an evaluation by a licensed professional in an appropriate specialty to determine the child's needs.
Our district has had some questionable requests from parents as well, and vision therapy seems to be a "hot" topic. For some disorders, it seems to be a legitimate avenue. For others, not so much. We are fortunate to have a well known pediatric opthamologist in our district and his decisions are trusted.
Not that vision therapy is the only issue, though. We have a local chiropractor who tries to get accomodations for all sorts of nonsense, including hearing "disorders" and asthma. Our audiologist sorts thru the "hearing disorders" and we require a physician or APN to certify accomodations for medical issues.