That instructor did so many things wrong he should get a Darwin award. Plain and simple... his range etiquette was sloppy. He handed a kid a fully-automatic weapon. He stood next to her, not behind her. He was not wearing a ballistics vest. (not required but certainly a good idea when handing a kid a fully automatic weapon) Honestly, that dudes family has nothing to complain about other than that guy being too stupid to be around guns.
You do make some good points.
However, I don't think wearing kevlar would have stopped the bullet from penetrated his head. The girl told her family that she was uncomfortable shooting the weapon and that she had bruises from shooting it (shoulder stock). Hindsight is 20/20, but I agree that the fault isn't with the gun range.
1.) no common sense age legislation for firing automatic weapons
2.) the instructor didn't exercise extreme caution and safety measures
3.) the family ignored the 9 year old girls complaints of shooting/not wanting to shoot
All of those excuses won't bring the man back and are independent from the gun range. I pray for the family, but I don't think they have a case.