This situation is a prime example of distraction, and blinkered attention, where both pilots are so focussed on the rare task at hand (that they must make an emergency landing), that they lose situational awareness of basic flight items. The problem here is that they did not conduct incorrect actions, as one option suggests, because they will have followed the procedure for the emergency landing prep as normal, which probably does not ask the pilots to check fuel levels. This was an "error of omission", where the pilots forgot to do something that they needed to do, which was to check the fuel. The pilots correctly conducted the actions that they made (as far as we know), they just missed actions like checking the fuel, which will likely have been a memory item.

The pilots became overly focussed on the emergency and lost situational awareness, and became distracted. This is taught in flight school, but is a natural error of the human condition that we must learn to overcome. Tools such as TDODAR, the decision making process, include reference to "time", which is absolutely limited by fuel remaining, and should have been a consideration to this flight crew.

To address the other options, the crew would not "rely" on a low fuel indication, and so it is irrelevant whether it was serviceable or not. This scenario is, unfortunately, very easy to do, as distraction and "tunnel vision" on a task is something our brains do very regularly, that we have to fight.