What gets me is the dad is head of some emergency medicine operation. That would indicate to me that he's not a Neanderthal in the brain department. So the fact that this could happen while he was present is really mystifying to me.
No, not a Neanderthal, but doesn't make him an expert in automatic weapons, or weapons in general. Having been involved in aviation safety, I know doctors and lawyers can afford "toys" in which they are not expert, don't have/get the training they should have, and can get themselves in situations beyond their ability to deal effectively. Perhaps he was new to the Uzi and that's why the instructor was there. And they allowed the child to play w/ Dad's new gun.
In any respect, it's a sad situation for the family and the instructor. And yes, the antis will use it to their advantage.