To me, it reads like they interpreted the noise/vibration from the aircon system as an engine failure, shut down the suspect engine, but due to the damaged throttle assembly shut down both engines, and did not have enough time to restart either of them.
Or, they interpreted the noise/vibration from the aircon system as an engine failure, shut down one engine (not knowing which one it was that "was" making the noise), then (when the problem did not go away) they shut down the second one but before the first one restarted (which would seem a bizzare error) and the damaged throttle assembly is a redherring. And did not have enough time to restart either of them.
Does that make sense to CJ pilots here?
If both engines were OK after all, they could have just ignored the racket and landed back. Were they getting odd engine instrument indications?