Hi wildsky! In a way, yes there is some truth to his fear. Any electronic device ( it's not true to routers only) can create its own EMF ( Electromagnetic Field). When exposed to it for a long period, it can become harmful to one's health.
If he has wired devices only and doesn't really need the wireless function of the router, he can disable that feature. He just need to access the setup page of the router to do that. It would depend on the model number of the device though as some wireless routers do not have that option.