I'm not sure how the record-keeping works for fueling. Certainly the pilots get a copy of the loading info. I imagine that whoever paid for the fuel gets a copy of the bill if nothing else. It is important for flight crews to have a good understanding of how much fuel is onboard - level sensors tend not to be very accurate so the most accurate figures come from measuring how much goes in and out.
If the plane has too little fuel the results are obvious. If it has too much fuel the results might not be as obvious, but it can be a big problem. Fuel is heavy - a plane needs more takeoff thrust or distance if it has more fuel, and it needs more landing distance if it lands with extra fuel (indeed, if a long-range flight has a problem right after takeoff they often end up circling or dumping fuel before landing just to shed weight). In order to maximize engine life the crew calculates the necessary takeoff thrust based on weather, weight, and runway length/slope, and programs the autopilot to deliver just that much thrust. If their weight was significantly over, they could run out of runway (especially if they had to abort at what they thought was the last possible moment - which would turn out to be too late - the crew calculates what that threshold is on every flight as well).
They certainly could put some max limits on range. A 777 fully fueled and fully loaded (that is, every seat taken and every baggage compartment loaded to rated capacity) couldn't take off at all. Long-range flights cannot carry as much cargo as a result.
So, based on what was in the plane they probably have a decent idea of what the range is. They probably don't know within 100 miles, but I doubt they'd be off by much more than 1000. Now, one thing the search radii doesn't reflect is winds - the effective range will be much less upwind, and much longer downwind. Obviously the max range is only achievable if the plane flies a direct route, and all that climbing/descending reduces range as well - max range can only be achieved at an optimal altitude (which starts out at one level and slowly goes up as the plane burns fuel).