Well, I am, to be blunt, pasty. A friend once told me I was the whitest white person he'd ever seen. I am very, very white.
When I was a kid and there was no such thing as sunscreen (just suntan lotion!! Oh my!), I used to have to wear a t shirt to the beach all the time. Swimming, playing, didn't matter. I had my dorky cotton t shirt on all day over my bathing suit (EXACTLY what a self conscious pre teen girl needs!) and I still burned. All the time - every year my shoulders would blister and scab...
Granted, that hasn't happens since the 70s, and I've found good sunscreens that keep me from burning, I wear long sleeves when I hike...if I don't BAD things happen...but who knows if all that "special" UV treatment of my running and hiking shirts actually do anything.
Just my experience...no actual facts here.