At least the Marine Pure 'Owners Manual' on BRS links to a study dated 10/2/12 says they conducted a study that found 'MarinePure bio-media was able to eliminate significantly more harmful ammonia and nitrites and convert it to nitrate'. With regard to nitrate removal, they say 'Nitrate removal is beyond the scope of this experiment, but it is usually accomplished by water changes, plants & algae using it as fertilizer, or another class of bacteria (anoxic) converting the nitrate to nitrogen gas which will leave the tank'. This is the only study I could find on Marine Pure's site as well.
BRS did some testing in one of its 'BRS Investigates' videos with inconclusive results but, all tanks tested, including the control, which was just a glass aquarium with no filter, live rock or sand of any kind, ended up at about the same nitrate level at the test's conclusion. One interesting possibility is that while the nitrate in the water column may have been the same in both tanks, the 'control' may have had more nitrogen tied up on bacterial bio-mass while the Marine Pure could have removed it from the system. But, who knows?
Ultimately, it would seem that the 'proof' of any nitrate reduction is anecdotal at best. I would think the company would be strongly motivated to prove Marine Pure's nitrate reduction potential if it could, so, I would guess they've tried but simply can't demonstrate any significant nitrate reduction, but, maybe I'm too cynical.
I realize we do many things in the hobby based on anecdotal evidence but, I think it is important to recognize when we're doing this and be careful about suggesting things are scientific fact or are proven through reliable studies.
Matt