While this initially seems impressive (i.e. 1 in 1,000 products are fake), Amazon has a power-law distribution to its sales, and thus likely to its views [1] [2].
This means that, as long as the products on the left side of the power-law aren't counterfeit, this claim can be true.
As a result, if you venture into niche product spaces, beware that you're looking at much higher odds of a counterfeit.
[1] http://ebusiness.mit.edu/research/papers/2010.09_Brynjolfsso... [2] https://www.marketplacepulse.com/articles/marketplaces-power...