I recently installed a new GFCI device in a kitchen. It was wired per the Option B which involves 2 cables or four wires. The electrical box is grounded so I didn't install a separate grounding wire. It tests good but when I plug in a two prong fan, the GFI trips. Or sometimes I can get it to stay on, but then it trips when the fan is unplugged. I can't see it being wired any other way.
Does your GFCI trip when you plug in a lamp or another type of device? It sounds like the fan is causing nuisance tripping within the GFCI when the fan is turning on and turning off causing an imbalanace between the neutral and hot current.