That statement is just lunacy. IMO, it is good advice to NOT believe anything Brightwell claims without independent verification.
ALL reef tanks and ALL parts of the ocean are organic carbon limited for bacterial growth. All that means is that if you add organic carbon, there will be more bacterial growth. If that were not the case, such as in a reef tank that was totally stripped of something the bacteria needed, corals would also not get what they need and would already be dead.
If one did have a carbon limited situation (say, bacteria in seawater lacking any dissolved organics), how does that cause dosed nitrate to be consumed extra fast?
Just ignore that statement and dose more or feed more, and when the Neonitro runs out, switch to sodium or calcium nitrate, food grade from amazon or elsewhere. It is cheaper and comes with a purity assurance that Brightwell does not provide.