Hmmm. Most often in residential wiring, the ground wire and the neutral (white) wire are electrically the same wire. If you look in your fuse or breaker panel, you might notice that the bare wire from the street is hooked to both.
If the fan is made of metal, the manufacturer of the fans might have their cases connected to the neutral wire, and if this is the case it is extremely important for the wiring to be properly polarized. This is why plugs are polarized, with the neutral prong being wider than the hot prong. The screw portion of lamps are supposed to be connected to neutral while the bottom center is connected to the hot leg.
When you unscrew a light bulb, you lose contact with the bottom center contact of the lamp after a half a turn or so, but the screw section remains in contact until the very end, and if that connection was made to the hot leg, there would be a danger of someone electricuting themselves touching it.
Bill