As a Korean it is funny to see this in HN. And yes, almost everyone used to believe this so that my parents always taught me turning off the fan before sleeping. This psudo-theory is so widespread that it is used to assassinate someone in fictions.
The younger generation don't believe in fan death anymore. Still, many of the older Koreans that believe in fan death are very well educated. However, talking to my parents, they were not educated to think critically, and even today that is not a value that is stressed in Korea. Essentially the majority of older Koreans were raised in a society which had dictatorships, coup d'etat, assassinations, censorship, and government controlled media. Koreans had great economic success, but less freedoms, similar to the situation in China today. Questioning the status quo is detrimental, and keeping your mouth shut is a virtue still taught in Korea today. Knowledge such as fan death is just accepted as fact, and it stayed engrained until recently.
Follow up: while critical thinking isn't encouraged or taught, does knowledge of the widespread usage of fans and the lack of associated deaths elsewhere ever come into conflict with their worldview?