The rationale behind this regulation is fire safety. The refuelling procedure generates enough fuel vapours to saturate the atmosphere surrounding the refuelling zone, rendering it flammable and explosive. At which point a spark is all is needed to ignite the air and the objects within it. This applies to all types of flammable-liquid refuelling -- aeroplane, motor vehicles, etc.
Igniting Fuel Vapours
A variety of explanations, and metropolitan legends, can be found on the topic. The most popular being static electricity. Accumulated static charges cause a potential difference between the charged material and its surroundings. This potential difference in turn generates an electric field, which, depending on its strength, can generate an electrostatic discharge, in the form of a spark. Turns out, electrostatic discharges can ignite fuel vapours.
This is the case for radio antennas which can output high amounts of power, thus generating a strong electric field. This can cause a spark to jump from the antenna to the electric ground. Now imagine an aeroplane acting as a huge antenna, being grounded at the moment in which the refuelling nozzle touches the tank.
Research on mobile phones generating static charges when in use is however inconclusive. One one hand several scary memos have been produced in the past years, warning people that using their phones while refuelling their car will cause explosions. However all these texts fail to explain how a mobile phone could ignite fuel vapours. This myth was even busted, not so long ago.
Nevertheless, mobile phones are forbidden around refuelling areas because they are not intrinsically safe. Normal operation of electronic devices generates small sparks within the circuits and components. Intrinsically safe devices are certified to comply with certain standards by rendering them incapable of generating enough energy, electric or thermal, to ignite its surrounding flammable atmosphere.
Another possible explanation for mobile phones ban in refuelling zones is due to the possibility of generating a spark between the battery poles and the connecting plates. This risk is amplified when the mobile phone is dropped and the battery detaches from its support.
Are We Being Paranoid?
Now whether regulations are being too over-protective is open for debate. Personally I would not risk becoming a human torch, just to prove them wrong.