People have been in trouble for giving OTC painkillers to friends for years now. Kids die because they aren't allowed to carry their own inhalers (this is policy at many US schools too, not just Canadian ones) Boy with Asthma Dies After School Confiscates His Inhaler
My nephew's Epi-Pen is kept with his teacher, and the only reason that she has it is because he's a little child and he can't inject it himself anyway, he needs an adult to help him. As soon as he's old enough and has the dexterity to do it as well as the ability to recognize the symptoms in himself he will have it in his bag and a spare with the teacher, no matter what the "rules" are.