RE: what would you have done
Well at 14 the young man should have known better than to shoot at a deer that had already been shot. If they were visible to you then they certainly knew that someone had already shot that deer.
I probably would have let him have the deer also but he would leave there knowing that what he did was not the smartest or most sportsman like thing to do. His father, or who ever was the responsible person, would have left there knowing also that teaching this young man to act like he did was certainly not in the best intrest of hunters and the hunting community.
Nip it in the bud. If it isn't corrected early on then he may just continue acting like this and one day it could turn ugly. We have all heard the stories of this very thing turning violent and even deadly.
Do you let your dog or someone elses dog piss on your floor and not correct it? Let it piss once and it will continue pissing on your floor cause it thinks it is ok to do so. But if you correct it from the start it will figure out that it ins't in his best intrest to piss on your floor and perhaps he should quit doing it.