The live from the light switch may just be a signal line but it is capable of drawing sufficient current for the unit to overheat and catch fire. It wouldn't normally but then again, the permeant live would not short-out in normal circumstances either. I.e. the point of the fuse is to offer protection in all excess-current circumstances. E.g. if the motor were to fly apart and short out the power on the signal live or something. So I would argue that the fuse needs to cut of all potential sources of power from the device.
Anyway, from your comments I'm concluding that the 3 amp fuse doesn't offer much in extra safety, but may be necessary to comply with regulations.
BTW, my main concern would not be claiming on the price of the fan if it melted, but if the overheating fan burnt the house down and the insurance company quibbling that it was my fault as I hadn't wired the fan correctly.