Heh... It's as accurate as a site that offers "every zip code". Where does weather data come from? Does every zip code have a weather station or an airport or some other location that gathers data? Of course not. Just because a site says the real city's name when looking up a zip code does not mean that it is getting data from that exact city. It gets the data from the closest place that has data. Sites that don't use the exact city name allow you to see exactly where the data is coming from. This allows you to see how far away the data is from where you're looking.
If that's all you were doing when you were getting the same weather data, was to look at all the zip codes in a small area, then it's normal. Try !weather 12345... You should get a place in New York.