All denitraters available on the market and DIY units all get the same water out of the tank. Some require feeding them directly. None of them have a special requirement that says low oxygenated water only into the unit to work that I’m aware of.
It's not about "low oxygenated water," it's about low oxygenated media. The bacteria that "eat" nitrates, do not thrive, in a well oxygenated environment. The bacteria responsible for Denitrification requires an anoxic environment. This is similar to Crushed Coral vs. Aragonite sand. Water is more able to flow through CC, due to the larger particle size of the media. Because of this, you'd need a much deeper bed of CC, than you would of Aragonite sand, to still create an anoxic (low oxygen) and anaerobic (little or no oxygen) environment. This is also why DSB (Deep Sand Beds) in our refugiums are recommended. A 1" sand bed, in our display tank, is not deep enough to create the proper environment, for denitrification to occur. We make up for this by creating the proper environment, by the use of a DSB in the refugium.
On of the best "Denitrification devices" involves a 5 gallon bucket 2/3s full of aragonite sand, with water SLOWLY moving through it, before returning back to the display. This is typically referred to as a Remote Deep Sand Bed. It was originally used, and brought to our hobby's attention, by Anthony Calfo.
Canister Filter, Wet/Dry Filters, Bio Balls, etc. all do a great job of converting and breaking down ammonia. Unfortunately, they're useless for breaking down nitrates, since they are an aerobic environment.
Here's a few excellent articles, that explain this in more depth, and may help us understand.
http://reefkeeping.com/issues/2008-04/newbie/index.php
Here's a great one. I've copied and pasted a couple of important paragraphs, that explain it, in a pretty easily understood way.
http://reefkeeping.com/issues/2008-05/newbie/index.php
"Beds need to be deep enough so that zones are created in the bed. The upper levels have decreasing oxygen tension, and organic compounds are processed by aerobic bacteria. Lower in the bed, oxygen approaches near depletion and bacteria use the oxygen contained in the nitrates, produced at the upper levels, to further degrade organics but using the oxygen from the nitrate molecule. This anoxic zone is where denitrification occurs and is the main reason for having a DSB in the first place. Four inches is the suggested depth, but having slightly less usually doesn’t hurt. Extremely deep beds, on the other had, run the danger of becoming fully anaerobic at their lower levels. That is not an ideal condition and should be avoided. Even at 4-6” there are some anaerobic areas in any sand bed, but those over 10” are more likely to have substantial zones. This invites conditions where sulfates can be reduced to toxic hydrogen sulfide.
One of the necessary conditions for a bed to be successful is that it has a continuous turnover caused by sand-shifting organisms in the bed. This means that sand should be fine enough for these organisms to move about. Very fine sand can actually be moved around by the combined efforts of the bacteria in the bio-film on the sand. The other reason for fine grains is that they provide a far larger surface area than large grains, thereby supporting greater organic loading. Having sugar-fine sand or finer is therefore far better than having something, like crushed coral, for the bed.
As I explained above, it is desirable to have zones of decreasing oxygen tension existing in the bed. It takes time for these zones to develop, so we want to keep them intact. Adding large sea cucumbers, large burrowing fish or big starfish, which can all disturb the bed, should be avoided. So should using one of those sand vacuums, so popular for cleaning substrate in a freshwater tank; they should be avoided unless it is just used to clean the very top of the bed."
Finally, here's another great article, part of which contains the following, which I also copied and pasted here.
http://reefkeeping.com/issues/2002-06/dw/index.php
"Like live rock, sand also works as an excellent denitrification filter when a bed of four or more inches of sand is used.Sand is so efficient that denitrification can even occur on a single grain of sand."
In the same way that we need a deep sand bed, to create anoxic and anaerobic environments, while Live Rock does help, with denitrification, the majority of it occurs deep within the rock, instead of on the surface.