I'm not sure the problem would be as hard to fix as the author of the article suggests, at least as far as paperback books are concerned.
There are only a certain number of POD services out there. The only way this scam makes a profit is if someone goes with a cheap printing operation rather than one of the well-known PODs, all of which are going to have similar printing costs. It ought to be possible to design an algorithm that identifies books from an unknown POD and flags them. (Amazon knows where the new paperbacks it lists come from.) Another algorithm could check the flagged books for any similar author name/title combinations. In that way, a relatively small number of possible scams could be identified for investigation by a live person.
One thing Amazon has been relatively good about in the past is responding to DMCA takedown notices. So if anyone does spot a counterfeit book being marketed on Amazon, that's definitely something to report and get fixed. Probably, the hassle will be minimal.