You are quite right that some people are allergic to certain things such as nuts and even milk to name two. Once diagnosed that they have an allergic reaction to something or an allergy it really is up to the sufferer to to be aware of their condition and how to manage it. In the case of a very young sufferer they either don't attend a normal school or stay at home and have tutoring there although that can be a abused, hence the need for two or more medical examiners.
As for someone being allergic to WiFi either they are either lying or have some other problem, usually psychosomatic but if this type of allergy is true then they are destined for a very short life since WiFi is pretty much everywhere in most cities around the world and I can't see it being removed for one or two people.
As an aside I wonder if the child's parents have a WiFi router at home or do they have smart phones.?
Good grief it won't be long before we have litigation on the dangers of mobile phone usage and how dangerous it is to be speaking on one when you are filling you car with fuel... Oh Wait!