"Light is electromagnetic radiation. Does she melt like she looked at the Ark of the Covenant whenever someone shines a light bulb on her?"
Probably not, but most of us would probably just get only annoyed by a flashing bulb, whereas some people would suffer epileptic fits. Nothing to do with the amount of heat/light, but the flashing repetitive change in levels.
While I suspect EM sensitivity is all in their minds (and they have a curious resistance to proper experiments that could prove their case because they say they don't want to suffer the symptoms in the name of science!) I keep my mind open to the small possibility that in rare cases there may be something in the brains of some people that does indeed respond to strongly pulsing fields. It definitely needs a lot more study to show whether they suffer what they believe they're suffering from. And even then, all we have is an absence of proof rather than a concrete disproof.