How does the pilot know that the amount of consumed fuel equates to a true distance traveled rather than a distance traveled according to the Round Earth coordinate system?
The round earth coordinate system has nothing to do with measured distances by an object travelling at a given speed for a given time.
The plane would need to know how fast it is traveling.
Airspeed indicator devices are not accurate and are not used in navigation. It is not possible to create an odometer for an airplane to guess how fast it is moving through the air. It is measuring fluids traveling within fluids. The airspeed of fluids against the wings is only used in things like banking maneuvers.
Groundspeed indicators which measure against the ground (such as GPS) are based on a Round Earth coordinate system, and would produce a Round Earth result.
Tom how do you travel? Im going to assume you have been to somewhere new, that you don't have inherent knowledge of where everything is. How did you get from point A to point B? Can't use a map, MapQuest, Google, any sort of GPS, or any modern technology as it is all based on RE measurements.
So, how the hell did you get there and back? Also did you tell whoever was on the other end of the trip, "I'll get there when I get there because I have no clue as to how far it actually is."