I would take a small bet that there is no statement in a B777 manual that could be reasonably interpreted as meaning the above.
Absolutely correct no Boeing manual does but it is certainly suggested in this article in Aero 8 from 1999.
The unreliable airspeed procedures supplied in the nonnormal section of the QRH have been expanded significantly for the 747-400, 757, and 767 and will eventually be expanded for other current-production models. The procedures contain a reference to indications, which can be individual discrete indications or engine indication and crew alerting system (EICAS) messages that basically point out the evidence of unreliable airspeed/Mach. Other examples of this evidence are provided in the QRH, such as
Speed or altitude information not consistent with pitch attitude and thrust setting.
Airspeed/Mach failure flags.
Blank or fluctuating airspeed displays.
Variation between captain and first officer airspeed displays.
Amber line through one or more PFD or ADI flight mode annunciations.
Overspeed indications.
Simultaneous overspeed and stall warnings.
The 777 system is a complex design that addresses these malfunctions. With only one bad source or failure, the system automatically switches away from that source, and the crew will not notice any difference.
My bolding. But we are in furious agreement on the need for pilots to practice their manual flying skills and for PICs to exercise their responsibility when the need arises.