Given that animals can also get skin cancer from excessive sun exposure, I think your basis for this belief is flawed.

Also not burning in the sun doesn't indicate anything, not everyone gets sunburn and it doesn't mean your skin cells DNA are not being damanged and increasing the chance of cancer.

Prehaps more relevant to modern life is the ozone layer was vastly stronger in the past which filtered out the damaging frequencies.

Stay out the sun!

I always hear this about allergies and I vehemently disagree. I grew up on a rural acreage a half mile from my grandfathers farm. Between home and the farm I was constantly exposed to all the allergens someone can be exposed to - horses, cows, cats, dogs, pollen, you name it, I spent a bunch of time with it starting from birth. I was and still am allergic to all of it.