I can't comment on the Airbus 'bird' and I don't remember much from the 737 NG, but the 777 FPV uses both inertial data and air data inputs from the ADIRU/ADM. Therefore if you have an unreliable airspeed situation Mr. Boeing says not to use it because the displayed information by the FPV MAY be compromised. May and not will, but if you follow incorrect data and it is not picked up by either of you by crosschecking pitch/power through different flight phases (and possibly in very high workload situations), then it's no good is it? Pitch-power, nail it and hold it with minor and smooth adjustments.
Somebody asked why does it need air data? I'd love to know as well, if anybody has any idea about it, please share it.