The Boeing QRH was only recently modified because of concern regarding misinterpretation of FMC fuel predictions in non normal configurations.
I have a great deal of sympathy with this crew - the Captain states that he was told to 'trust' the fmc . In my experience, this is a common emphasis in glass cockpit training. Pilots are being intentionally 'dumbed down', and the emphasis is on the infallibility of modern aircraft systems.
Surely we must return to using 'common sense', i.e. airmanship?