In South Korea most fans have timers so they're not left on overnight, because people think it'll kill you if you do leave it on.
This belief wasn't helped by medical examiners putting "death by fan" on the death certificates of suicide victims to help the dead save face and spare the families the embarrassment of a "cowardly death" for a few decades.
That's basically what they think, yes. That it interrupts the flow of the air, as if capillary action was needed to pull air into your lungs. I'm not sure how the myth started but at one point they were selling fans with special guards or something to protect against the imaginary risk.
Of course, I might be wrong - I read about this on the internet.
I used to work in a real sweatbox of a factory so we had huge fans running all day. It was deceptive because you'd normally be drenched in sweat but the fans prevented it. So you'd drink a gallon of water and take maybe one brown ass dehydrated piss. I could see something like that being blamed on a fan. Just heat exhaustion or dehydration