Is the sun's damage to skin sufficient to warrant protection anytime the average person goes outside or just for extended periods?
Because the website you link speaks of cancer, they probably go by the rule that a single exposure and even a single photon of UV may be sufficient to cause that one mutation in that one skin cell that will eventually lead to cancer.

In the end, they are right, because mutagens (UV, cigarettes, radiation) do not follow typical toxicological rules. There is no threshold dose of UV that does not cause cancer, as even a single short exposure may do the trick. Obviously, multiple exposures and longer exposures increase the chance. This, as opposed to toxic substances that generally feature a threshold dose. Below this threshold dose they are considered harmless.