To answer yours question Melanin adds a resistant factor to it, but the actual sunburn is caused by actual damage at the cellar level from UVA and UVB rays.

Think of Melanin more like sunblock in that it extends the amount of time before noticeable damage to the sun will happen. While the time for sun damage to accumulate to be what you would call a sunburn might vary from person to person, everyone is still susceptible to UV damage.