The mapping zip codes to city is not strictly 1:1. I don't have a better source for this, but the description in Wikipedia states:

"The Postal Service designates one _default_ place name for each ZIP code... Additional place names may be recognized as _acceptable_ for a certain ZIP code."

This means that someone may continue to write their address as Smalltown, EG, 12345, when technically it is Bigtown, EG, 12345. Of course, this would not be the case with zip+4, which like the UK postal code system, identifies a much smaller grouping of addresses.

[1] http://en.wikipedia.org/wiki/ZIP_code#ZIP_codes_and_previous...