As I understand it the risk is two-fold:
1) During a fault the grounded receptacle has the potential to energize grounded metal parts of an appliance, and there is nothing to clear that fault.
2) With BX the fault current will try to flow over the metal armor. Because the BX does not have a bonding wire, the armor will heat up much like a light-bulb filament. This is a potential fire hazard.
I'm not really sure if grounding each receptacle to the box is illegal. It doesn't appear to violate 406.3, especially if the receptacle yoke is in solid contact with the box.
However, at the panel, I would GFCI protect all the BX circuits with grounded receptacles, to comply with 406.3(D)(3)(c)
-John
