Do you regularly use coffee for nasal rinses? In the context of the post, tap water is safely sterile. No water is ever perfectly sterile, though deionized, triple-distilled water comes close.
Your other points are sound, but this one is rather ridiculous. The air in an average home already contains several kilograms -- not grams, but kilograms -- of water, all of it aerosolized from outside your home, an environment far less sterile than tapwater.