I have heard this several times, and it just can't be true. In a liquid, things move from areas of high concentration to areas of low concentration. If you put a drop of dye in a glass of water, a minute later, the dye will be evenly distributed throughout the glass of water. And that's without circulation in the glass.
You will not have higher concentration of nitrates, or ammonia, at one level in the tank than at another level in the tank. Take your water sample from wherever it's convenient, it will read the same as at the bottom of the tank, or the middle of the tank, or the top 2 inches of the tank -- doesn't matter.
It's diffusion. I learned that in college chemistry. Even did math problems calculating how long it would take for a solution to diffuse through a membrane -- and then there was "osmotic pressure", diffusion can cause pressure.