This is retarded. I have excessively sweaty hand (not the wrists the hands), and have hand many multi-hour/multi-day gaming sessions. I'm talking putting on 50 hours of game play on good old FFVII in a few days. With my excessive gaming and excessively sweaty hands, I have never, ever had this problem. EVER.
I'd say the only person dumber than the parents, for letting their daughter play to the point of "red, sore lumps on the palms of the hands," is the doctor for thinking that this is caused by gripping the controller too tightly. If anything, I'd blame this on the girl being allergic to the plastic from the controller. It makes more sense, and by running a few test it can easily be proven.