On Fan Death, the media bought it all up and publicized it on TV, naturally most South Koreans believe it. They are super conscious about anything related to health (even though smoking and binge drinking is quite common here).
If I have a cold, my wife (Korean) will tell me to go to the hospital. I grew up with not taking medicine unless it's absolutely necessary.
Back on topic, It's more of a culturally thing. I wouldn't bother trying to explain to people that it's not real, focus on feeling amused about the cultural difference.
Likwise, I'm from Australia, in my hometown (small beach town), I could walk to the local convenience store wearing no footware, no tshirt - just boxer shorts. To Korean people, they'd think I'm insane..... Just trying to highlight the differences in culture; seeing the humorous side of things is often better than trying to persuade someone they're wrong.