Per Denver, I went and checked out Prof./Doc. Lomborg's site. Lawsuits are less fun and more expensive than an abscessed molar, and the definition of fair use is as lucid as a Dvorak article. It looks like Lomborg copied and displayed the whole Scientific American piece, thus making a fair use argument much tougher. Here's a nifty reference to help illustrate: the "fair use checklist" that Indiana University provides its researchers.* It lists the factors a court is likely to consider in determining whether the copying is a fair use. Note that using a whole work and making it available on the web are big "cons." A case study from the same source also is informative, as it works through hypotheticals involving a professor's reproduction of a magazine article. Where the use is non-profit and the purpose is sufficiently worthy, even wholesale copying can be a fair use - you'd have a tougher time convincing a court, but it could be done. Even so, Being Wrong Loudly can be a remarkably effective legal tactic, especially before a court is involved. The Prof./Doc. probably decided this was not the place to plant his flag and squander his resources. He still gets his digs in without using the whole article.
(*Here are similar faculty guidelines from Bryn Mawr and Vassar.)