A very pale person may burn in 5 minutes. It doesn't make sense that your body would speed up the synthesis of cholesterol just because your skin has less melanin or is more sensitive to UV radiation. Also keep in mind that no matter how much is synthesized it's up to the liver and kidney to make it into a useful hormone.
> The lightness adaptation enhances calciferol (vitamin D) synthesis. Too much epidermal melanin for the latitude blocks UV penetration essential to the dermal synthesis of calciferol or vitamin D.
If you have less melanin then more sunlight reaches the lower layers of skin which increases vit D synthesis.