The statement, in my opinion, seems to draw heavily on classical "FARMS-style" LDS apologetics, even citing work from well-known apologists such as Daniel C. Peterson and Ugo Perego, who has a Ph.D. in genetics. I had dinner with Brother Perego in Rome recently (I'm in Rome as I write this, about to visit the Vatican) and am pleased to see that his work has played a prominent role in this important statement from the Church. His own DNA results are mentioned in the article (turns out his mitochondrial DNA points to some of the same Asian roots found among many Native Americans, though he has no known Asian connection in his ancestry).
For those of us who have dealt with the Book of Mormon challenges raised by our critics based on DNA studies, this statement is much appreciated. I also like the implicit hat-tip to classical scholarship-based LDS apologetics. This statement comes from the Church and required lengthy review and scrutiny from the Twelve, as I understand. So nice to see it published. May we learn from it and consider its multiple healthy implications.
Update, Feb. 3, 2014: The FAIR Blog has a good discussion of some implications of the new statement.