The short answer is that some church leaders and others have commented on this subject, with various points of view taken.
On the one hand, some point out that those who witnessed the translation process testified that no materials were used in the translation. For instance, in "The Last Testimony of Sister Emma," first published in the RLDS publication The Saints' Herald volume 26, number 19, Joseph Smith's wife gives the following in response to questions on the subject of the translation of the Book of Mormon:
Q: Had he not a book or manuscript from which he read?
A: He had neither manuscript nor book to read from.
Q: Could he not have had, and you not know it?
A: If he had had anything of the kind he could not have concealed it from me.
Others, however, argue that a Bible was likely used in the process. A passage from B.H. Robert's New Witnesses for God, part 2, volume 3 (see this link for an electronic copy) most clearly takes this point of view. Pages 425–440 quote a letter with a very similar question addressed to Joseph F. Smith, sixth president of the LDS Church, and Smith's response, which begins with the following statement (p. 427):
"The difficulty which you point out [referring to the verbatim nature of the quotations] of course has been recognized by believers in the Book of Mormon, but I do not know that I can say that the Church as yet has settled upon any explanation which could be regarded as an authoritative view on the subject."
However, Smith then goes on to offer his own opinion for the similarities (p. 429–430):
"It should be understood also, in this connection, that while Joseph Smith obtained the facts and ideas from the Nephite characters through the inspiration of God, he was left to express those facts and ideas, in the main, in such language as he could command; and when he found that parts of the Nephite record closely parallel passages in the Bible, and being conscious that the language of our English Bible was superior to his own, he adopted it, except for those differences indicated in the Nephite original which here and there made the Book of Mormon version of passages superior in sense and clearness. Of course, I recognize the face that this is but a conjecture; but I believe it to be a reasonable one; and indeed the only one which satisfactorily disposes of the difficulty you point out."
In addition, there are also some leaders and scholars who have stated that Joseph Smith's use the language of the KJV was a choice, while remaining somewhat more agnostic about the exact process behind how that wording was put in the translation. For instance, LDS scholar Hugh Nibley outlined his thoughts on this in response to a letter to the editor of the Church News in 1961 (reprinted in The Prophetic Book of Mormon, ed. John W. Welch, volume 8):
As to the "passages lifted bodily from the King James Version," we first ask, "How else does one quote scripture if not bodily?" And why should anyone quoting the Bible to American readers of 1830 not follow the only version of the Bible known to them? Actually the Bible passages quoted in the Book of Mormon often differ from the King James Version, but where the latter is correct there is every reason why it should be followed... Since the Book of Mormon is a translation, "with all its faults," into English for English-speaking people whose fathers for generations had known no other scriptures but the standard English Bible, it would be both pointless and confusing to present the scriptures to them in any other form, so far as their teachings were correct.
In addition, in the 1966 edition of Mormon Doctrine (p. 302, entry titled "King James Version of the Bible", electronic copy here), Bruce R. McConkie appears to take this stance:
Joseph Smith read, respected, reverenced, and taught the King James Version "as far as it is translated correctly." (Eighth Article of Faith.) Whenever he found Biblical quotations in the Book of Mormon (they having been copied from the brass plates and preserved by the Nephite prophets), he rendered them into English in the exact language of the King James Version, except in instances in which the language of that version did not convey accurately the original thought.