I think you've got the law right, but I don't think that'll help prove fair use here.
Taking an article that is used to generate advertising revenue and reposting it somewhere that the author will not receive any revenue from goes firmly against the "commercial value of the original work" prong of the fair use defense.
Consider the equivalent: let's say I run a "non-profit" website, hypothetically just a blog where I generate no income, and I repeatedly copy articles from behind the NY Times paywall onto my site. That's copyright infringement and is substantially depriving the NY Times of their income for the articles. I believe I would lose a fair use defense there. I think the situation is the same if I copied NY Times articles that were not behind the paywall because they would be able to show that they were losing ad revenue.