The problem is't going from OFF to IDLE right away. The engine won't spool down fast enough to get below 13% N1 by the time you get to the boldface, even if you are doing it slowly. The problem is going above IDLE before the engine has properly spooled up to 67% N1 (Flight Idle). During an airstart, the PMU does not manage the ITT, torque, etc. like it does on the ground. If the PCL is pushed up too early, fuel is introduced at a rate faster the the engine can burn it. This creates a very big heat flash melting and warping the blades in the engine. With the number of blades in the engine and the precision required for it to run, it doesn't take much to completely destroy the engine. I wouldn't be surprised to see a 4th step to the boldface in the next -1 change to wait until flight idle N1 before pushing the PCL past the IDLE position.
The crew did not perform a Turn Climb Clean Check but they were never on profile for a suitable landing surface. The IP did a lot of things wrong, but by the point the irreversible damage was done, there was no place for him to put it down. Don't pin that on him too.
This is not a problem with the PT6. It is a problem with the design of the engine cutoff. Imagine an inexperience IP sitting in the back, arms on the rails, and he sees the student turn into lead with way too much closure. Depending on the range and closure rate, adrenaline starts to pump and he lurches forward to grab the PCL. If he overshoots by 1/2", he can easily hamfist the cutoff gate and rip the PCL back to OFF. This isn't an uncommon occurance. I've heard of several inadvertant shutdowns in the T-6 for this specific reason (at least 3 at Laughlin since I've been here). Most don't make the news because immediately pushing the PCL back to IDLE usually relights the engine. Supposedly there is a fix in the works to make the PCL cutoff a two-handed device but it's not going to come online for several more years. (unverified)