I've heard that daddy longlegs are extremely venomous, but they can't bite humans because their fangs are too short to penetrate the skin. Is that true?
First of all, there are actually three kinds of critters called daddy longlegs. The common name daddy longlegs is most often used to describe Opiliones, aka harvestmen. Opiliones are arachnids, but not spiders. They have no venom glands at all, and are absolutely not venomous. The nickname daddy longlegs may also refer to a crane fly, which is a true fly and a member of the order Diptera. Crane flies do not pose a threat, either.
Sometimes, the name daddy longlegs is used for another group of arachnids, the spiders of the family Pholcidae. These spiders are also called cellar spiders.
Cellar spiders do have venom glands. However, there is no scientific evidence whatsoever to confirm that their venom can harm a human being. Not a single documented case exists of a person being bitten by one and having an adverse reaction.
Pholcid spiders do have short fangs, but not any shorter than other spiders that have been known to bite humans. The cellar spider's fangs are similar in structure to those of a brown recluse spider, which we know can and does bite humans. Again, there is no evidence or proof to the claim that their fangs are too short to bite a person.
In fact, the show Mythbusters tackled this daddy longlegs legend back in 2004. Host Adam Savage subjected himself to a cellar spider bite, proving that the daddy longlegs spider is indeed capable of breaking human skin. The results? Savage reported nothing more than a very mild, short-lived burning sensation. Analysis of the daddy longlegs' venom revealed it's nowhere near as potent as venom from a black widow spider.
So, you really don't need to worry about daddy longlegs, of any variety.