That's a cute fairy tale.
In the real world, over 5.6 million tons of nitrogen are applied to corn (40% of which is feedcorn, on top of 40% for ethanol. barely any for us vegans!) each year through chemical fertilizers, compared to a mere million tons of nitrogen from manure. A good amount is coming from cattle, like you said, but the reality is that the clear majority is artificial.
And regardless of whether it's natural or artificial, nitrates then wash into the rivers and waterways causing algae blooms, fish die-offs in rivers and lakes, drinking water pollution, ocean dead zones, coral bleaching and other habitat destruction, that shit even gets into the groundwater. In the human body it causes cancers, thyroid disease, birth defects, and probably more we don't know about.
Poison isn't better for you just because it's "natural" 🙄