It's called passive nitrate control. The use of fine deep sand beds (DSB) and large quantities of live rock has made nitrate issues manageable or non-existent is many aquariums. This is because a complete nitrogen cycle can be achieved.
In a nutshell: Waste is mineralized by Heterotrophic bacteria to ammonium. Then Autotrophic bacteria, Nitrosomonas europaea, oxidize the ammonium to nitrite. Nitrite levels rise and Nitrospira-like bacteria (Autotrophic) multiply and oxidize nitrites to nitrates. Nitrospira-like bacteria grow at a very slow pace and populate slower than Nitrosomonas europaea. This is why the 6-8 week wait when starting a tank. Ammonia toxicity is the number one killer of aquarium fish; nitrite is number two. So far in this nitrogen cycle the fuel for growth of the bacteria is carbon dioxide.
This is where most of us are stuck - with high levels of nitrates. We can use protein skimmers, do water changes, and grow macro algae. I'm a proponent of all of the above. Attempts at making denitrifying equipment have come short because they have a tendency to create sulfide; sand beds in the 2" - 3" range can also. The topic at hand is why a sand bed above 1 1/2" and less than 3" can be detrimental.
To complete the nitrogen cycle we need to achieve denitrification by dissimilation, which is the breakdown of nitrate into nitrogen gas; which is done by bacteria in low oxygen zones (DSB's and rocks). Denitrification bacteria quickly uses up all available oxygen and are forced to use nitrates as their food or carbon source.
Nitrates can also be assimilated by growing algae and harvesting it. And, there is assimilatory denitrification, vodka and biodegradable polymers, which harvests the assimilated nitrates (and phosphates) through the use of a protein skimmer.
The optimal depth of a fine deep sand bed is 6". The minimum depth required for fine sand is 3". Aragonite has a half-life of approximately 18-24 months, it can dissolve at a PH as high as 8.2. Which is a wonderful benefit of having sand and the reason to make the sand bed deeper at the start. The dissolution of the calcareous sand is a source of minerals, like calcium and carbonates, for reef growth. These compounds are liberated when the substrate becomes acidified.
If the sand bed is under 3" in depth increasing levels of oxygen penetrate the sand bed and shifts the biological faculties from denitrifying to nitrifying colonies. Sand between 1/2" and 3" is usually not deep enough to reduce nitrate and yet too deep to be fully aerobic. The nitrifying bacteria in the oxygenated upper region of the substrate will compete with organisms for ammonia and other nutritive compounds in the water.
Thus, finally, the answer: The nitrifying bacteria will colonize in the sand bed, compete with organisms for nutrients (and win), and they will not be in the water column where they can be exported.
Any questions, I'll be happy to answer them. It's late, so, I hope I didn't cut it too short.