I'm not sure that we do "accept DNA for genealogical research but not to prove the BOM tribe origins". The statement is a bit obtuse. That said, there are many reasons DNA is "useful" for genealogical research and there are many reasons current genealogical research actually fails to "prove" (or disprove, as it were) the Book of Mormon's account of Native American ancestry as has often been over-zealously been claimed. To accept something as useful and to say that something proves or disproves, are two completely different statements. Whenever one is looking at evidence and trying to discern some useful bit of information based on it, one must take into consideration what the evidence actually is, and how it relates to what one is trying to learn about. A similar problem occurs if you ask the question "why do scientists accept Einstein for the theory of relativity, but not to prove that we live in a deterministic universe?" Einstein's theory of relativity is very useful for making predictions and explaining observed phenomena, but arguments for a deterministic universe just haven't panned out. (Though I happen to think he was right on both accounts.)

All DNA evedance tells us that the BOM is false, end of story, LDS does not want to admit they have been living a lie.

It’s unfortunate that, when some random scientist that doesn’t even work in phylogenetics announced that DNA evidence “disproved” the Book of Mormon, it was all over the news; but when, just a few months later, a team of phylogeneticists and one of the United States’ most advanced DNA sequencing facilities used the very same “negative” evidence to actually *support* the Book of Mormon, there was virtually no press at all. Even most members of the Church are still unaware of the findings, which among other things, show a direct correlation between the X haplogroup found in only two modern populations: one a subset of Jews, another a subset of Native Americans. For lots of information on this topic, see http://www.fairlds.org/apol/ai195.html . My personal favorite is the last one, “Does DNA Evidence Refute the Authenticity of the Book of Mormon?” Regardless, I’m guessing this will be yet another falsehood that, 100 years from now, the so-called “anti-Mormons” will still be citing even though it will have been conclusively disproved over a century ago.