Are you sure?
Absolutely not right!
look here and make your own conclusions!
Trying to give skin pigmentation the most important factor for genetic correlation, is like trying to make assumption based on the most enviroment choosen genes.
Doesn't work.
Migration from the north?
1- South was allways more populated, there was not enough "nordic" people to change the genetic background of the southern people, even if there were massive migrations.
2-there was no one in the north 12000 years ago
I could go on and on...