google this article "nitrate in the reef aquarium by randy holmes farley" and it will explain.
you don't have enough chaeto biomass to outpace the nitrate your tank is producing, no matter how its lit or circulated. a very special dedication has to be made in order for chaeto to outpace the bioloading we keep in these tanks. nearly every biocube with chaeto in the back area, and every tank keeping chaeto in the front display, and most of them with chaeto in the sump, are not benefitting through nitrate binding even though they say they do, its just a fad.
If a little bit of growing chaeto was enough to clean up nitrate, he'd say that in the article. Having chaeto anywhere in your tank is perfectly fine, but it can't beat large water changes, skimming, and reduction of feed input into the tank, per that article.
The article says water changes aren't even the best way to accomplish nitrate reduction, check it and see. It does however work for me because in my small reefs I change 100% of the water and I control the feeding in a certain manner, so in this case large water changes certainly reduce my nitrates compared to overall bioload in the tank.