...The bodies of you or I could be defined as machines:
Link to the definition of "machine." That definition uses metal objects to illustrate what a machine is. This does not mean that a machine is made of metal, rock, or some non-organic material. The organs that sustain our life are machines.
By the way, Homo Sapien bodies will also just respond to stimuli, even if the consciousness of the owner doesn't feel it. You can pinch the arm of a sleeping person and they may flinch or jerk the arm away. However, were they in one of the deeper stages of sleep in which they were not conscious, they wouldn't have felt it, despite their body reacting.
For that matter, it's never implied that Vivi's body is made of metal or rock. We only know that the stagnant Spirit Energy of Gaia was compressed to form Black Mages' bodies.