Does DNA evidence directly disprove the Book of Mormon?

In "DNA reveals we are all genetic mutts", David Reich, a professor of genetics at Harvard Medical School, talks about how migration shaped human populations. The TL;DR for people who want to know the "yes" or "no" answer to my post title is: 

"It's complicated."

Read the article.

One question genetics can’t answer, he said in response to an audience question, is exactly how population replacement happened. “In the case of Britain after 6,000 years ago,” he asked, “did new people come in and kill the old ones, or just crowd them out? 

We just don’t know. What genetic data does is provide facts about movements of people and changes in groups. We are not the experts to describe how that happened.” 

One important takeaway from this study, he said, is that humans inherently derive from mixed ancestry.  

“No population is, or ever could be, pure,” he said. “Ancient DNA reveals that the mixing of groups extremely different from each other is a common feature of human nature. We do not live in unusual times; profound events have occurred in our past. We should learn and feel more connected from that.”

I don't feel particularly like going into the details of why people are wrong when they say the Book of Mormon isn't true is because Native American DNA doesn't have any Jewish DNA mixed in. It's all been covered in much better detail and depth elsewhere. So, enjoy the links below.

The Book of Mormon and DNA Studies

Basic principles of population genetics suggest the need for a more careful approach to the data. The conclusions of genetics, like those of any science, are tentative, and much work remains to be done to fully understand the origins of the native populations of the Americas. Nothing is known about the DNA of Book of Mormon peoples, and even if their genetic profile were known, there are sound scientific reasons that it might remain undetected. For these same reasons, arguments that some defenders of the Book of Mormon make based on DNA studies are also speculative. In short, DNA studies cannot be used decisively to either affirm or reject the historical authenticity of the Book of Mormon.

Upper Palaeolithic Siberian genome reveals dual ancestry of Native Americans

Our findings reveal that western Eurasian genetic signatures in modern-day Native Americans derive not only from post-Columbian admixture, as commonly thought, but also from a mixed ancestry of the First Americans.

Are all Native Americans descendants of Lehi?

The Book of Mormon itself, however, does not claim that the peoples it describes were either the predominant or the exclusive inhabitants of the lands they occupied. In fact, cultural and demographic clues in its text hint at the presence of other groups. At the April 1929 general conference, President Anthony W. Ivins of the First Presidency cautioned: “We must be careful in the conclusions that we reach. The Book of Mormon … does not tell us that there was no one here before them [the peoples it describes]. It does not tell us that people did not come after. [emphasis added]

DNA and the Book of Mormon

Joseph’s wife Asenath, daughter of Potipherah priest of On, is the ancestral mother of the tribes of Ephraim and Manasseh (Genesis 46:20). While her genealogy is unknown, there is no reason to believe that her mitochondrial lineage or that of her descendants, including the Lehites, would have matched that of the tribe of Judah. The presence of mtDNA types in Native Americans that do not match those found in modern Jewish groups is fully consistent with both Book of Mormon and Bible accounts. [emphasis added]