The fuel system engineers will follow this train of thought, I trust, based on the difference between volume-unit and mass-unit measurements. If I follow that AAIB reading of the data correctly:
1) Both fuel metering valves opened per (initially) autothrottle, and later manual command. Thus I'd exonerate all upstream control hardware and software.
2) The flow metering valve is typically a volume metering device, calibrated such that when a fuel has known density and BTU content, then a calibrated mass flow (and thus BTU rate) is delivered to the burner.
3) However - fuel flow, measured typically by mass-flow devices (someone update me if this is not the case on 777s), in this instance shows little or no increase in mass flow.
The only conclusion I can draw is the properties of fuel reaching the burner were quite abnormal, likely a high volumetric percentage of air or vapor, with drastically reduced BTU delivery.
And the next question I must ask is: What was the indicated metering valve position, and the indicated mass flowmeter signal, during the latter part of descent before the throttle increase was commanded?