The principle, as I understand it, is fairly simple: to grow and multiply, bacteria and plants need carbon, nitrogen, and phosphorous in relatively large amounts, as well as smaller amounts of other elements. In a perfectly balanced tank, there will be enough carbon so that the bacteria and macroalgae will be able to make use of most or all of the available nitrate. If carbon is limiting, then the other elements will go unused, and nitrate will go up.
It actually seems to work. Years ago, when I first started dosing kalk with vinegar (another carbon source), my nitrate went down rapidly. It had never gone much below 20 before vinegar, but went down to about 5 with it. I would not call it a scientific finding, merely an observation consistent with the theory.
I still dose vinegar for the seagrasses, to make sure they have enough carbon for growth. Cheaper than vodka, less likely to grow fungus in the dosing reservoir than sugar.