This urban legend is very well established in many English-speaking countries, including Australia.
Fact: First, we need to know which group of arachnids are being referenced. There are daddy long legs (also known as granddaddy long legs), which are not spiders. They are in the arachnid group called Opiliones. They have one major body part with eight long, spindly legs and do not make webs. The opilionid arachnids don’t have fangs or venom. They do have little pincer-like mouthparts for tearing apart vegetation or dead insects. They can give a little nip but they do not “bite” as we typically envision.
In contrast, daddy long leg spiders are in the arachnid group called Araneae; they have two major body parts with legs attached to the front body part and usually are found hanging upside down in webs. These spiders do indeed have short fangs and they are capable of biting although bites are almost unheard of; they prefer to scurry away. On the rare occasion of a bite, the effects are minimal as their venom is not very toxic to humans.