I've heard fan death is cited in cases where suicide or overdose is the true cause, and families don't want to admit it to themselves or others.
The Wikipedia article does have a citation from 1927 [1], though, so it would seem the origins are much older than that.
My guess is it's a bit of all of the above. Maybe there was a little bit of belief in it, and the government, but government efforts to reduce energy usage as well as families using it to cover up suicide or drug overdoses helped propagate the belief and make it far more widespread.