That actually could be a concern, especially if other kids come home from school feeling ill. There could be mold growing somewhere, like in the ventilation system or carpets. Or there could be a source of bacteria, or fumes from something. Removing the kids from that environment *would* cause an improvement.
Of course, the idea that Wi-Fi poses a health risk is ludicrous. Now, if they were against Wi-Fi because kids don't seem to be learning all that well, and computers and internet are present in more schools than ever--well, that would be a different matter.
Mold is another one of those things that gets over blown.
I grew up on a farm in the Midwest. Mold was all over outside in the barns and in the old houses.
Might be because we were exposed to it all the time.