What you say is logical, Matgallis, but there is another missing piece.
You don't see male pattern baldness in 13-15 year olds because their hair is not yet programmed to be receptive to DHT.
Consider this. All men go through puberty, right? But, NOT all men have male pattern baldness. ALL men DO have DHT being created in their bloodstream, DHT in and of itself does not cause male pattern baldness, it is only half of the problem. The main difference between male pattern baldness sufferers and non-baldies is that us male pattern baldness sufferers have hair that is genetically programmed to be susceptible to fall out at various stages of our lives. Other, NON-male pattern baldness men have just as much DHT in their blood as we have, the reason why they don't lose their hair is that their hair follicles' receptors are not sensitive to it. This same phenomenon is why us male pattern baldness sufferers lose hair in the temples and crown yet keep our back hair... the back hair is not genetically programmed to be affected by DHT.
I hope I described this with some clarity, it is hard to put into words cogently, but, I have studied male pattern baldness a LOT and I have a lot of knowledge on the internal biology of the workings of male pattern baldness.