A couple things stand out. You didn't hear their shot....or at least didn't mention that on here. So they were tracking it...perhaps for a distance. That means they were doing the right thing to try to locate that animal. Second you followed your instinct. You did the right thing by you and by the kid. From the wound you describe, it could have been a quartering away shot where they had reasonable expectation that the bullet would take out a lung. I have seen a couple folks say don't give the deer over because it will somehow teach a lesson to make a better shot. Maybe. But more likely it would be a memory for the kid of making a shot and tracking a deer and having someone else take it out of the woods.
The way you left it, there is much greater potential for positive lesson learned from the experience. I'd like to think I would have done the same thing.