.22LR can be made to fire in
fully automatic mode. There's even a .22LR Uzi variant just saying pick that caliber by itslef would not have been a sure way to have "avoided" the accident. Although the damage from a .22LR would have been considerably less than a 9MM, if the instructor got shot in the head due to muzzle rise in auto mode it probably wouldn't have mattered anyway.
At such a young age, I would think top priority would be to teach her aiming properly, familiarize with the kick back, how to properly place the butt of the weapon against your shoulder, don't pull the trigger with your entire finger, etc. and,... full auto would be turned off.
But, what is done is done, unfortunately. And, I don't foresee any rabble rousing to ban children from gun ranges - nor should there be, ever.
If anything, I hope other instructors would ensure they don't allow children to shoot guns that most likely will lose control over and keep full auto off. If the parent doesn't ask for .22LR ammo, then it would be wise for the instructor(s) to insist in doing so. Or, make it their policy, etc.