Possible scenario
The shut-down of both engines was obviously inadvertent. The PIC hears the vibrations and considers engine malfunction as the cause. Given his seating position it would be natural to try the left engine first. 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. In the limited time available he has to decide which one to restart. High workload in the cockpit. Within the time available he has one chance to relight the correct engine and climb away from 150ft. On his own that would have been a true feat of airmanship, all decisions made in an instant.
Now add two crew. Does PIC delegate engine restart procedure to PM or does PM as the more experienced pilot take control? Did PM offer to retard right hand engine before PIC could tell him that he inadvertently closed down the left hand engine?
AAIB do not speculate on the two crew issue so we have to assume they give it no relevance.
In all honesty who could predict that a faulty bearing in an ACM could lead to two engines being shut down, one inadvertently, whilst flying at 1,000ft agl?
Bad luck does some times play a part in accidents. The correct response to this bad luck is to try and eliminate as much of it as possible for future flights which the AAIB report attempts to do with its safety recs.