Why would fact checking anyone be distasteful? Well, for instance, if I'm understanding correctly what Friel claims, it's something like this: Lomborg makes lots and lots of citations; their relation to the material they're cited in support of is often unclear; it often turns out that they don't in fact support what he's saying. If that's true, then fact-checking him would be a lot of work because of the many citations, and the vagueness of reference that would require more work per citation, and the (hypothetical) fact that often the citations are no good. (Failed searches usually take longer than successful ones.)
Begley doesn't claim to be offering analysis. It's a book review. Do you seriously think it would have been appropriate for the review to be twice as long in order to go into more detail on each claim it mentions?
Anyway. You say Lomborg addresses "each of Friel's claims made in the book review" (weird way of putting it, btw). OK, let's look at the first one: what's happening to the population of polar bears. Well, er, the word "bear" doesn't appear in Lomborg's rebuttal. There's a bit about populations of penguins; nothing about polar bears. Oh. Next: heat deaths and cold deaths. There is certainly some discussion of this in Lomborg's rebuttal, but he doesn't seem to have anything to say about one of the most striking claims Begley says Friel makes: that Lomborg cites a study from 2006 as showing that global warming will save 1.4 million lives that would otherwise be lost to deaths from cold, when in fact the figure claimed in that study is 850k. Next: stuff about the Larsen B ice shelf. No occurrence of "Larsen" or "shelf" in Lomborg's rebuttal.
Your claim that Lomborg addresses every claim of Friel's that's found in the book review appears to be totally false. Did you read Lomborg's rebuttal, or did you just hope I wouldn't?
Incidentally #1: Why the quotation marks around "distasteful"? That word is yours, not Begley's (still less Friel's). Begley used a different term.
Incidentally #2: Why the quotation marks around "analysis"? My best guess is that it's because I used that word. But I used it about Friel's 272-page book, not Begley's 2ish-page review.
Incidentally #3: Why "book review / editorial"? It says "Book review" at the top. It is dedicated to describing and evaluating a book. Its author is not an editor. It's a book review; it's not an editorial.