Fish poop is "not" where a majority of ammonia (that ends up as nitrate) comes from.
Although the metabolism of all waste produces ammonia, ammonia is constantly exuded from the fishes gills, and is invisible.
This is why large, frequent water changes are so important.
The water in a fish tank is always being inundated with ammonia from fish urine.
As far as nitrate from the tap
I just checked the Philadelphia water companies annual report, the average highest nitrate is < 4ppm, (range for 2013= 0.730-3.8ppm nitrate) the MCL for any water producer in the US, is 10ppm.
You can check it (and any US city) by going to Philadelphia (your city) annual water quality report
Absolutely correct. Fish poop is primarily non digestible items. All animals are designed to eliminate nitrogen due to it's toxicity to animal organisms, and perhaps the most efficient method is through the gills. Terrestrial organisms use less efficient methods like urea, urine and feces because we can't exude it into the air from our lungs.