"Retarding left engine first doesn't rectify the problem. Unknown to him he has cut-off fuel supply to left engine because missing rivet head doesn't stop the throttle lever at the idle stop. He reapplies full left hand power and retards right engine.Due to no bleed air entering the ACM vibration stops. Believing he has rectified the problem he cuts fuel to right hand engine. Now he discovers he has two inoperative engines."
What your saying in a way it makes sense, but surely even if you only meant the left engine to go to idle but because of the missing rivet the engine shut down completely the master caution, hydraulic, fuel pump and generator lights would all flash pretty madly in your face as soon as the engine spooled down.
I could understand if it was the right hand engine they shut down first as a precaution as they believed this was the one causing the problem. When this didn't resolve the vibration they brought the throttle back on the left with the intention on only going to idle to see if this helped and then unfortunately found themselves with 2 engines shutdown .
What ever happened it was a very sad event.