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?
Or your behavior is different on a cloudy day? More covered in clothes, not sitting still in the sun at the beach all day etc.
I’ve gotten visibly sunburned on cloudy/foggy days, where it was completely overcast. You may have gotten lucky.
I think the point is just about temperature. I've experienced this out on lakes in the northern US for example. It's sunny but not like a tropical beach, and maybe even a little chilly. But you'll definitely get burnt without sunscreen
Geography has a lot to do with it as well. Proximity to the equator, altitude, etc.
The damaging part of sunlight is the UV (Ultraviolet) spectrum. This penetrates clouds more easily than the visible-spectrum light.
So sun obscured != low UV. It will block some of it though.