I think a lot of this "Don't trust common sense" and "Don't rely on human logic" kind of stuff is intended as a sort of jab at atheism (although it obviously backfires and ends up making people look like idiots).
A lot of atheists trumpet common sense and logic as the bane of belief in God, and instead of trying to disprove this erroneous assumption, people just say "ignore logic and common sense".
If it wasn't for logic, I'd actually probably be an atheist right now. The same goes for science, once I started studying science in college, I really started thinking "There's no way this could have all happened by chance." I wasn't an atheist before, I just didn't have very strong faith - and science, reason, and logic (and common sense) all helped to bolster my faith dramatically.