Shadow
As one who has worked in the oil & gas industry for some considerable time I hope I can contribute constructively. The subject is covered extensively by a number of standards. One of the most comprehensive is:
Institute of Petroleum, Model Code of Safe Practice - Part 15, Area Classification Code for Petroleum Installations.
There are others by BS, API etc, but IP part 15 is widely used.
As the title suggests it is primarily for use in the petroleum industry and covers Tankage, Bulk Loading/Unloading, Petroleum Jetties, Distribution & Marketing facilities as well as offshore installations and drilling operations. Aircraft fuelling is not specifically addressed (as it is undoubtedly covered by some specific publication) but no doubt can be treated in a similar manner.
Basically, the code provides a guide for the classification of areas around equipment handling or storing flammable petroleum fluids in order to provide a basis for the correct selection of electrical equipment.
Strictly speaking it applies to FIXED equipment but application to 'hand held' equipment is relevant.
In order to operate a mobile phone safely in a hazardous area it would have to certified 'intrinsically safe' ie where any sparking that may occur is incapable of causing ignition of any gas or vapour present. (Identification of the 'hazardous area' is what the code is for and depends on numerous factors)
To my knowledge no manufacturer has yet produced such a phone.
Many manufacturers have published information saying their products are safe for use near refuelling operations but none appear to have actually produced a CERTIFIED piece of equipment. No doubt because it is a costly process and they do not see any return on the investment required.
As has been stated by other posters the type of fuel (fluid category) has a major affect on the area classification, kerosene types requiring less onerous measures than more volotile fuels.
Bottom line?
Do not allow the use of mobiles, if only because allowing their use around one type of fuel could lead to complacency and lead to their use in a potentially dangerous situation.