JOEL - Many Latter-day Saints, both past and present, have perhaps incorrectly assumed that the Americas were totally unpopulated prior to Lehi's arrival, and that Lehi's decendents are represented by all tribes of the Native Americans. However, Church leaders have for a long time warned us not to make this assumption.
For example, in 1929 Anthony W. Ivins of the First Presidency told Latter-day Saints:
"We must be careful in the conclusions that we reach. The Book of Mormon teaches the history of three distinct peoples, or two peoples and three different colonies of people, who came from the old world to this continent. It does not tell us that there was no one here before them. It does not tell us that people did not come after. And so if discoveries are made which suggest differences in race origins, it can very easily be accounted for, and reasonably, for we do believe that other people came to this continent." (Ivins, 1929, p. 15) Ivins, Anthony W., LDS Conference Report, April 1929, p. 15.
Two years earlier, LDS scholar Janne Sjodahl wrote that “students should be cautioned against the error of supposing that all the American Indians are the descendants of Lehi, Mulek, and their companions” (Sjodahl, Janne M., An Introduction to the Study of the Book of Mormon, Salt Lake City:Deseret News Press, 1927).

From BH Roberts:
“Moreover, there is the possibility that other peoples may have inhabited parts of the great continents of America, contemporaneously with the peoples spoken of by the Book of Mormon, though candor compels me to say that nothing to that effect appears in the Book of Mormon. A number of our Book of Mormon students, however, are inclined to believe that Book of Mormon peoples were restricted to much narrower limits in their habitat on the American continents, than have generally been allowed; and that they were not in South America at all.” ---Letter to William E. Riter, February 6, 1922. Studies of the Book of Mormon, pp. 53-54.

Now, years later, some critics would have others believe that the Book of Mormon requires that all Indians descend solely from Jewish founders, and that this is the official teaching of the Church. They get this perhaps from the introduction to the 1981 edition of the Book of Mormon which calls the Jaredites, Lehites, and Mulekites, “the principal ancestors of the American Indians.” However, that phrasing is not found in scripture, was never used by Joseph Smith, and did not appear in any previous edition of the Book of Mormon. Other church leaders have specifically felt that different peoples also settled in the New World, as I explained above.
Increased knowledge about the Americas and improved understanding of the Book of Mormon text itself offers a better understanding. Nowhere in the Book of Mormon does it say that no one else was there when the Nephites arrived. The Nephite record certainly allows for other groups immigrating under direction of the Lord(2 Nephi 1:5), and explicitly states that the Nephites will be mixed with other peoples(1 Nephi 13:30). The latter may suffice to explain why Jewish-type DNA is so rare among indigenous peoples of the western hemisphere. The other races of people(possibly of Asian decent), who were already there, certainly would have been much larger and would therefore have dominated the genetic structure of later generations after intermixing with offspring of Lehi and Sarah. We should therefore not expect to find any MDNA from Lehi's family in today's generation of native Americans. The introduction of the new MDNA from the larger population, preexistent in the Americas, would prevent such a trace. This does not mean that at least some of the American Indians of today are not descendents of Lehi and Sariah; it just means that we might not be able to conclusively prove it one way or the other through MDNA testing. ( See the article: Genetic Markers Not a Valid Test of Native Identity)
Besides this, we also don't know if the original ancestors of the Lamanites(Lehi, Sariah, Ishmael and His daughters), possessed the unique and defining Middle Eastern traits and did not possess any genetic variants(perhaps from distant Asian ancestry?) that were atypical of the Middle Eastern genetic heritage. To be certain of anything we would need to test a sample of DNA from Lehi and his party, which of course is impossible.

The Jews in Jerusalem were descendants of Judah. The Book of Mormon people declare their lineage as coming through the Joseph who was sold into Egypt by his brothers. These two tribes claimed Israel as their father, but did not share the same mother.
A mother's DNA determines familial characteristics. Critics of the church ignore the fact that the Joseph who was sold into Egypt had taken a Gentile for his wife. It is illogical to assume there have been no intermarriages or other DNA influences in more than 4,000 years of world history.

The preexisting inhabitants were not described in detail in the Book of Mormon because the history is not about them; but a few hints of their presence can be found in the scripture. For example, Sherem was described as a man who "came..among" the early people of Nephi(Jacob 7:1), suggesting that he was a stranger. Jacob, a son of Lehi, also goes on to remark "that he had a perfect knowledge of the language of the people" (Jacob 7:4). Why would this be pointed out if he were already a Nephite? At the time of Sherem's visit, the entire population of Nephites decended from Lehi could not have exceded a few dozen adults. Any Nephite among such a small population would not have been a stranger. So if he was not a Nephite where did he come from?
Towards the end of the Book of Mormon the prophet Mormon declares:
"I am Mormon, and a pure descendant of Lehi. I have reason to bless my God and my Savior Jesus Christ, that he brought our fathers out of the land of Jerusalem," (3 Nephi 5:20)
The fact that he had to specify that he was a "pure" decendent, suggests that he knew that there were "unpure" decendents caused by the intermixing with other races.
Statisticians have also calculated that it would be nearly impossible for the population of the Nephites to have grown to the large numbers in the time allowed without taking in others into their society who were already there.
Murphy is facing possible excommunication from the LDS Church, not because of his DNA research, but because of his accusations that the LDS Church has racist beliefs about the Native Americans; and his claims that the Book of Mormon was a work of fiction; and for open attacks on other aspects of Church doctrine, working closely with those who want to damage or destroy the LDS Church (See the article: Motivation, Behavior, and Dissension). When a member starts publicly promoting ideas that seek to justify their non-belief or encourage non-belief in others, as Mr Murphy is doing, the Church is within its rights to separate those persons from the body of the Church, based on open and harmful apostasy(Church Handbook of Instructions, p. 95). Please see the article The Parable of the Chess Club and Anti-Mormons.
The LDS Church has no fear of DNA studies. In fact the largest and most extensive study of DNA evidence and the America Indians is taking place with millions in privately donated money at Brigham Young University.
(See the article: DNA and the Book of Mormon).