That's correct. The nitrifying bacteria that use ammonia and nitrite aren't limited by lack of organic carbon. If they were, you'd have elevated levels of either, or both.
Denitrifying bacteria (convert nitrate to nitrogen gas) are limited due to lack of low O2 areas, not organic carbon. This is why people often see high nitrates. Again, adding carbon won't increase their population.
I came across this article... quite interesting:
http://www.oscarfish.com/article-hom...-bacteria.html