Well, of course Bayesianism is your friend here. Probability theory elegantly supersedes the qualitative concepts of "knowledge", "belief" and "justification" and, together with an understanding of heuristics and biases, nicely dissolves Gettier problems, so that we can safely call "knowledge" any assignment of high probability to a proposition that turns out to be true.

For example, take the original Gettier scenario. Since Jones has 10 coins in his pocket, P(man with 10 coins gets job) is bounded from below by P(Jones gets job). Hence any information that raises P(Jones gets job) necessarily raises P(man with 10 coins gets job) to something even higher, regardless of whether (Jones gets job) turns out to be true.

The psychological difficulty here is the counterintuitiveness of the rule P(A or B) >= P(A), and is in a sense "dual" to the conjunction fallacy. Just as one has to remember to subtract probability as burdensome details are introduced, one also has to remember to add probability as the reference class is broadened. When Smith learns the information suggesting Jones is the favored candidate, it may not feel like he is learning information about the set of all people with 10 coins in their pocket, but he is.

In your example of the book by Mr. X, we can observe that, because Mr. X was constitutionally compelled to write truthfully about his mother's socks, your belief about that is legitimately entangled with reality, even if your other beliefs aren't.