Kirchhoff's Voltage Law

I understand the general rationale behind this law. However, a statement on page 79 of Electricity Demystified confuses me:

Kirchhoff's Voltage Law arises from the fact that a potential difference can't exist between any circuit point and itself! A corollary to this is that a potential difference can't exist between any two points that are directly connected by a perfect conductor (that is, one that has theoretically zero resistance).

I had thought that there is an inherent potential difference between the substances at the anode and cathode of the battery. Connecting those with a wire (even a perfect conductor) would not cancel this potential difference. What am I missing here?