From my experience as a driver all drivers except freight are contracted out. Contractors pay for gas and vehicles.
Fed ex as a whole shouldn't really be losing on gas prices, only penalties for not delivering packages (it was $100 per package a day that was failed to deliver) that is levied on the contractors but thats the extent of my first hand knowledge.
I should add fed ex does have their own fuel yard so in a way they might have some susceptibility to gas prices but i think prices are still pushed on to contractors still.