There have been incidents in the past where pilots have been unaware of their low fuel status because of a fault in the indication syste, - or have been unable to believe their fuel indicators because they don't make sense. AIUI most modern airline control systems now compare fuel measurements with fuel estimates, as a discrepancy between the two can imply a fuel leak, but this isn't universally the case.
In fact, having just read the AAIB preliminary report, it makes no mention of either engine shutting down (as would be the case if the fuel had run out), but merely that
At approximately 600 ft and 2 miles from touch down, the Autothrottle demanded an increase in thrust from the two engines but the engines did not respond. Following further demands for increased thrust from the Autothrottle, and subsequently the flight crew moving the throttle levers, the engines similarly failed to respond. The aircraft speed reduced and the aircraft descended onto the grass short of the paved runway surface.
It's not explicit, but it implies not that the engines shut down completely, but that they failed to provide an increase in thrust required to make the runway. Stranger and stranger!