I'm always a little wary of situations where people use Dr. in their title (except for Dr. Pepper). Anyway, the science is sound behind anoxic filtration however his design is pretty terrible. What you need to do is deplete the oxygen in the system as fast as possible to generate anoxic zones, so you would never leave it open to atmosphere. What he doesn't seem to mention is what happens to the nitrates in the system. There are really two paths that it could take, first it could be converted back into ammonia which his test strips convenient don't test but would explain his decent plant growth. Second it can be converted to nitrite --> nitric oxide --> nitrous oxide --> nitrogen (gas). But the absence of bubbles in his system makes me think that he's just converting stuff back and forth.