Highly unlikely an entire chain of military personnel knew it was a school and was like, "yeah get em good, and lets see when they come scrambling in for their kids corpses".

Do you hear yourself? Have you ever in your life met someone this sadistic? It was definitely a mistake. One might argue criminal negligence, but there is no way everyone in the loop here is just pure evil. That just isn't how people think in North America. It is unfathomable that a team of US military (people with families of their own no doubt), would all nod along and agree with your contention.