The question that arises in my mind is;
If this rivet was broken some time before the accident flight and this caused the throttle to bypass the gate, I am surprised that no one else experienced an unintended shutdown of the engine previously.
Most pilots I know place the throttles "solidly" in the idle position on landing. This ensures no excess residual thrust and (for those that have it reverse can be selected). Therefore if this rivet was missing for some flights the natural solid closing of the throttles when landing would have produced the same results as the closing of this throttle during the accident flight would it not?
In fact I would expect that the throtle was placed against the gate several times duting the taxi out on the final flight. Did it work perfectly on all those occasions but bupass the gate on the single occasion that it is closed (smoothly in best practice) as a result of suspected engine vibration?
I think that faced with unsure source of engine? vibration I would close one throttle and if that had no effect I would open that one again before closing the other.
As anyone who has flown the citation knows, even in a well trained multi-crew environment the RHS pilot can only monitor the LHS pilot's actions because most of the important switches are on that side of the cockpit. Therefore the best way in which the RHS "mentor" could have helped is fly the aircraft and maintain orientation to the runway or best forced landing area. This is what did not happen and the reason they traveled to an area that they did not want to fly to is that most probably no one was looking out the window.