The article cites DNA studies that claim Native Americans, from North, South, and Central America are descendents of Asiatic peoples -- consistent with the traditional Alaska land-bridge theory of migration. Some find this troubling, expecting to find some DNA evidence that would link Native Americans to those of Jewish ancestry which would be supportive of the Book of Mormon narrative. Unfortunately, there are those who have left The Church over such studies. And as usual, some of the harshest critics of the church are from apostates. Some apostates have even gone so far as to call upon the church to "apologize" to Native American peoples, and Polynesians for having "lied" to them about their true heritage.
In response to the article, The Church has posted the following on its website:
The Book of Mormon: Another Testament of Jesus Christ is exactly what it claims to be -- a record of God's dealings with peoples of ancient America and a second witness of the divinity of the Lord Jesus Christ. The strongest witness of the Book of Mormon is to be obtained by living the Christ-centered principles contained in its pages and by praying about its truthfulness.You can read The Church's response, along with links to several papers that defend the Church's position with regard to DNA studies and the Book of Mormon here.
Recent attacks on the veracity of the Book of Mormon based on DNA evidence are ill considered. Nothing in the Book of Mormon precludes migration into the Americas by peoples of Asiatic origin. The scientific issues relating to DNA, however, are numerous and complex. Those interested in a more detailed analysis of those issues are referred to the resources below.
There is an LDS Blogger, Jeff Lindsay, PhD, who frequently discusses historical and physical evidences of the Book of Mormon. His Blog is called Mormanity, in which you will find some interesting reading. He also has a more formal website called LDS FAQ, which answers questions about the LDS Church. If you look at the link above to the Official Church website, you will notice that one of the articles referenced for further information on DNA and the Book of Mormon is by Brother Lindsay. The paper is rather long, but you can read the short summary of the paper here. You can also access the full-length paper from this link as well.
As for me, my testimony of the Book of Mormon is not based on physical evidences, or scientific studies. The Book of Mormon is a spiritual document, and to be understood, it must be understood by spiritual means. I have read the Book of Mormon several times. I have earnestly prayed to know of its truthfulness, and I have received my own witness, many times over, that it is the Word of God. Building the foundation of your testimony of the Book of Mormon by spiritual means is like building upon the Rock of Revelation.
Those who build their testimonies by intellectual means, by physical evidences, or upon scientific studies are building the foundation of their beliefs upon the sand. The next big archeological finding, or scientific study that seems to be in conflict with the Book of Mormon will cause the sands to shift upon which they have built their "intellectual testimony".
In this life, there will always be questions that will have to go unanswered for now. The supposed conflicts between DNA evidence, and the story of the Book of Mormon will one-day be answered. Maybe not in this life, but ultimately the answers will come. It is similar to other questions we have about science and religion, such as: the creation, the dinosaurs, evolution, and geologic time vs. biblical time. We know that one-day, after the Second Coming, all the books will be opened, and everything about the earth and its inhabitants will be revealed from the creation on through to the end of the earth.
Our belief in the Book of Mormon is meant to be a matter of faith. ". . .For ye receive no witness until after the trial of your faith." (Ether 12:6) From time to time our faith might be tried and tested. That's part of what we agreed to when entering mortality. The Book of Mormon was never intended to be a history book. It was never intended to be a mere archeological relic. That's one reason why we don't have the Gold Plates displayed in a museum today.
The Book of Mormon has always been intended first and foremost to be a witness of the Divinity of the Lord Jesus Christ. It carries with it the fullness of His Gospel. It is intended to persuade all men to accept Jesus Christ as their Lord and Savior, and invites them to come and follow him. No scientific study will ever change the true purpose and meaning of the Book of Mormon. In the due time of the Lord, any seeming conflicts will be resolved, and those who have been deceitful and made false allegations will be revealed for who and what they are as well.