The strawman goes something like this: The Book of Mormon is obviously not a direct copy, or is not obviously just a plain old plagiarized ripoff of a given proposed book, therefore the theory of a connection between the Book of Mormon and the ideas in that book is comprehensively disproven.
The problem is that nobody is saying that Joseph Smith just wrote the Book of Mormon as his own version of "View of the Hebrews" and that the Book of Mormon is really just a derivative work of it. Nobody is saying the Book of Abraham is just Joseph Smith parroting the words of Dick, as if he were "copying" Dick in the Book of Abraham.
Nobody's saying this. This is just a straw man.
What people are saying is that the Book of Mormon came about in a time and region of America where certain themes were being discussed, including in some books that Joseph Smith likely had access to, and that it was from this religious milieu that Joseph Smith picked and chose some of the ideas of his theology.
It would be like Joseph Smith winning an award for the Book of Mormon and Book of Abraham, and while accepting his award, is asked who some of the authors are that influenced his work, and he might have said well Ethan Smith was one influence, and Thomas Dick was another, and Swedenborg was another, and Solomon Spaulding's work had quite an affect on me, and some things I heard a Campbellite minister preaching about really had an effect on me, and so forth.
I haven't had a chance to really dig into the Stephen Lesueur book yet, but I did get a couple pages further in between innings during the last two night's Red Sox victories. I found this very delightful description which I think is one of the best ways of saying this concept that I've yet seen.
The religious concerns of these ancient Israelites paralleled those of nineteenth-century American Protestantism, and the Book of Mormon discusses many of the same theological issues (infant baptism, faith versus works, the nature of God) that preachers and revivalists frequently debated in upstate New York.
The critic of the Book of Mormon would say "yeah, and there's a very good reason why the Book of Mormon just happens to parallel the religious concerns of nineteenth-century American Protestantism, and there's a reason why a lot of the same things debated by revivalists and preachers in upstate New York during Joseph Smith's youth also happen to be in the Book of Mormon." It's that the Book of Mormon is a product of the 19th century, and is Joseph Smith's resolution to these debates, and that his theology is an amalgamation (Lesueur actually says this) of a lot of things that were believed or taught by various people during that time period.
Did Joseph Smith derive his theology from just one source? No! Was Joseph influenced by various specific people's teachings during this period? Undoubtedly, and the whole Ethan Smith/Solomon Spaulding/Thomas Dick/Swedenborg/Sidney Rigdon stuff demonstrates that clearly.
ps: when I say "Joseph Smith", I don't mean to imply that I think the Rigdon/Spaulding/Cowdery connection in terms of the writing of the Book of Mormon aren't possible. I don't know whether Joseph created it alone, or whether he got by, at first, with a little help from his friends. That the theological ideas come directly out of the 19th century though is, I think indisputable. Well, it's disputable by those who need the Book of Mormon to be true, but it ought to be indisputable. ;-)