It's not a contradiction if/when you understand what's going on. The claim that Purigen removes organics that contribute to ammonia-->nitrite-->nitrate does not mean it removes same already in the water. So for example, if you already have high nitrates in your tank, Purigen will do nothing to remove them.
However, bear with me as I tell my story and my personal experience with these products...
I have very high nitrates (40-80ppm) in my well water, most likely due to the 95 acre farmers field across the road. This means that I have to filter my well water for partial water changes to remove the nitrates. This is labor intensive so I looked for any and all means to keep tank nitrates low in the hope that I could reduce the volume of weekly water changes and still have pure water for my fish. Before migrating to a planted tank....
I switched from gravel to sand fearing the gravel trapped waste producing nitrates. I was not overstocked. I fed carefully and I religiously serviced the filter to remove detritus. I used two pouches of Purigen in my 60g. Hoping to culture anaerobic bacteria to convert nitrates into nitrogen gas, I added another Aquaclear 70 filter totally filled with nearly 2 liters of Seachem Matrix & DeNitrate (Matrix and DeNitrate are a pumice stone [a type of lava rock] with deep pores claimed to be able to support anaerobic bacteria. I later built another filter with nearly 4 liters of Matrix & DeNitrate and seeded repeatedly with Seachem Stability (Claimed to contain faculative, aerobic and anaerobic bacteria).
AT NO TIME was I able to reduce the tank nitrates to desired/acceptable levels....and I tried for about 2 years! Are the claims exaggerated? Who can say for sure. It would require some very serious research lab work to make such a bold claim. I can only report my personal experience and simply say they did not work for me as advertised. Was I doing something wrong? Maybe, maybe not.
So 2-3 months ago I migrated to a heavily planted tank and am hoping that the plants will assist in keeping tank nitrates low and tank water [more] pure. The Matrix/Denitrate is in the garage - the filters now just use foam, bio-foam, and polyester filter floss.