I’ve always wondered about this. I have fair skin, and I tend to burn somewhat easily in very sunny environments like the beach.
However, I’ve never gotten so much as a whisper of sunburn / suntan / anything on an actually cloudy day where sun wasn’t hitting me directly. Is the damage a different type that’s imperceptible? Or is this a public health comms strategy where they assume people will see a single cloud in the sky and decide it’s fine to skip sunscreen, so they talk about how you should slather yourself with sunscreen 24/7, even if the sun is obscured?