A psychosomatic illness (i.e., one originates in the mind, but that impacts the body) can have very real impact on the body. A person who is so inflicted, and who is given what he believes to be a cure, may very well achieve a restoration of health. But I do not recommend getting into the health care business here. If you get a contract to install a device, and if your warrantee is restricted to the installation alone (i.e., not the health benefits of the installed system), then you would be acting within the legal and moral limitations of the profession. I, for one, would want nothing to do with such a project.
I think the person is ill. I think that nothing an electrician, or an electrical engineer for that matter, can make the person better. I think that once you are at least 6 inches away from an NM wire that is carrying current, the magnetic fields generated by the two conductors will have cancelled each other out, and can have no impact, adverse or beneficial, on a person nearby. I also think that no amount of scientific proofs will be able to convince this person that the wiring system is incapable of giving him the relief that he seeks.
I have no idea what a Balanced Voltage System might be. But I would bet good money (no more than the price of a minor confectionary, of course) that it is not a miracle cure for this person?s illness.