Tracking down the history of the myth has been difficult. This is mainly due to much of the research and sites dedicated to debunking myths like this focus on the myth and not where it started. But I have found several common threads in my research.
Several state the myth started in the 1970's with a National Geographic where the focus was on the life of a Daddy Long Legs spider. During the documentary the hunting and food preference were reviewed and showed daddy long leg spiders hunting and eating other spiders such as the black widows.
With National Geographic showing a small spider hunting, killing, and eating these poisonous spiders its believed that people began to think "If it can bite and kill a black widow it must be more poisonous"[4]. With the thought that it's poisonous but no reports people getting hurt they had a short leap to the thought that "maybe their fangs are to small".