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The ground is a safety feature. It should never carry any current but
if there is an imbalance between the live and neutral, the ground will
carry the excess current to "ground" instead of letting the excess
destroy your electric device.
If the ground is carrying any current, it is indicative of a program
somewhere in the system.
>Second, if this rule DOES apply to AC, why does it not
>apply to batteries (DC)? If I place some batteries on the
>ground (or connect either terminal to the ground socket of
>an AC plug) they do not discharge.
Actually, they do discharge. However, they are discharging through
the air which has an incredibly large resistance so the current drain
is incredibly small so it will take a very long time for the batteries
to discharge. This is why many batteries have a "shelf" or "drawer"
life rating.
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