The third person in the scenario really is key, that is why real captains (
) never touch the wheel or throttles of the ship that they command. Although a well trained person does a lot of their job unconsciously, that unconscious effort of keeping the wings level, fighting the stick shaker, scanning the gauges, etc. takes a lot of processing power that would otherwise be devoted to reasoning. You have much more ability to control things if you stand back and let others do the grunt work, which is also why admirals aren't up on the bridge directing the captain how to maneuver his ship to conform to the general battle plan.
One would have to be very bright indeed to reason that the nose is sinking because of a malfunctioning computer system (yes it was a malfunction even if it didn't throw an exception) who's existence violated every bit of knowledge that you have about how your plane works, and the first crew did not in fact figure that out.
On a more prosaic level, my wife who does not have much knowledge of things mechanical or electrical has often been the key to solving a difficult mechanical or electrial problem. "Don't you usually connect both wires of your voltmeter when you are testing a circuit?" When you are hanging upside-down covered in diesel and barking completely up the wrong tree electrically that extra pair of eyes, even if nontechnical, can spot the "obvious". Even a pax may have been able to note that there was a pattern to when the wheels started spinning down, something that many here seem to assume would have been easy to notice while sirens are going off, pax are screaming, and you are pulling with all your might on the control stick. Of course, it is highly unlikely that airlines are going back to having an engineer, although this particular failure is one in which an engineer would have most valuable.