If Amazon had direct liability for selling counterfeit products, for example, if the Ove Glove company (first in the original article) could sue Amazon and recover all the revenue that went to the counterfeiters plus a penalty - I believe in this case Amazon would find a solution to ensure supplier verification.

The problem is that currently it's profitable for Amazon to host goods from fraudsters; if (when) any get discovered, they kick them off but keep the proceeds. Society and law should ensure that Amazon loses money when hosting goods from fraudsters, so that the motivation is properly aligned.