No argument at all that nitrate is being generated, but there are kinetics involved in each of the reactions involved in converting ammonia to nitrite and then nitrite to nitrate. In general we want these kinetics to be fast enough that we do not see an accumulation of either ammonia or nitrite in the water. In a typical aquarium these kinetics are heavily influenced by the total surface area available for the bacteria that perform these reactions to "live".
My point is your accumulation of nitrite and/or ammonia is obviously not what you want in the end, regardless of the debate on the toxicity of nitrite in water.
