But how could Joseph have known ____?

This is an often-used counterargument to evidence against the divine origin of the Book of Mormon, Book of Abraham, etc. Take a look at this recent article, for example, in which apologist Daniel Peterson uses it (and twists some of the evidence to support his conclusions.) Hugh Nibley employed a similar strategy of looking for historical events and cultural practices that line up (often spuriously) with LDS claims, and then claiming that Joseph couldn't have known about them, so he must have been inspired.

Essentially, this kind of argument is a way of side-stepping contradictory evidence because you just can't fathom how Joseph could come up with something like the Book of Mormon out of whole cloth. This is a fallacy, as it assumes that if the Book of Mormon isn't divinely inspired, then the only other option is that he made it up himself, with no help. In actuality, there are plenty of sources he could have gotten much of the Book of Mormon from. It's not my job to explain where it came from; if it's logically inconsistent with our world, then it's clearly not historical, and I'm not obligated to speculate on its origin any further.

Still, such arguments are flawed in another fundamental way: they lack a null hypothesis. If you're going to argue that Joseph got an unusually high proportion of "hits" or things he couldn't possibly have known himself, you need a standard of comparison. Even a blatant con could expect to get things right or "almost" right here and there. You'd need to know that Joseph got more things incidentally right than a known conman could expect to get, on average, were the conman to attempt to create a pseudo-religious document. Without this information, you're just showing that you don't know much about cons, the ability of some people to pull them off, and our general capacity as human beings to be duped.

Take, for example, the curious case of Frank Abignale, the man portrayed by Leonardo DiCaprio in Catch Me if You Can. This man is famous for writing fraudulent checks and later conning his way into jobs as an airline pilot, a medical doctor, a lawyer, a professor of history at BYU, and many others.

Now, consider the high frequency of "hits" Frank would've had to use to get these jobs. A case could be made that Frank actually was an M.D., a lawyer, etc. (he actually passed the bar exam in Louisiana!) simply because he knew enough to pose as them. Such a claim would be absolutely ludicrous, but equally so is the claim that Joseph Smith, who clearly mistranslated the Book of Abraham, got enough "hits" or "near hits" that he must've been right about everything else, ignoring the fact that he was provably wrong.

There's also Mark Hofmann, whose skill at forgery and ability to invent documents that mimicked early church history was sufficient to fool the first presidency of the church into buying his creations and then defending them publicly. Eventually, of course, everyone learned that Hofman's creations were not historical. Yet, clearly there were enough "hits" in the content that top leadership deemed them credible.

For other examples, take a look at these amazing feats. How easy would it be to argue that none of these things could have happened without direct divine intervention?

This style of argument is common, because it provides a way to avoid dealing with uncomfortable evidence directly, and it seems to be highly effective. Many Mormons seem to be sold on the idea that Joseph couldn't possibly have invented the Book of Mormon or Book of Abraham (even with help from his contemporaries.) Then again, Mormon-dominated Utah also seems to have an amazingly high tolerance of multi-level marketing business models, so maybe it would be helpful to start demanding a higher standard of proof before extending trust.