zip codes used to be a service mark. they are not "public domain", they are an identification of a private corporation and are OPTIONAL in the united states: see Domestic Mail Services Regulations, Section 122.32. They should only apply to the places that fall under the jurisdiction of the District of Columbia.
As far as my limited knowledge of the subject goes, US has 2 separate laws, and 2 separate jurisdictions - State and Federal. There are people who fall under one and not under the other. People who do not fall under the "Federal" commercial law, will use addresses without a zip code.
A Postal Service is "quasi-government" agency, i.e. a private corporation, just like Federal Reserve. Zip Code™ does not apply to addresses that fall under the jurisdiction of a State only - as in 50 states of the union, excluding District Columbia, Puerto Rico, Guam and a couple of other territories.