Don't think skin color would apply here. Even Punjabis has two types dark, medium and fair skin (almost Caucasian ish). I'm a fair skinned non-tamil, and have always been mistaken as a medium shade Punjabi. My family comprises of all shades too, akin to Malay/Chinese people where everyone comes in different skin colors.
Implying North Indians are fair just by Bollywood is big no. Just look at travel channels, you'd get an idea.
Sauce : have Punjabi friends, and various ethnic non-tamils acquaintances and also worked closely with India Indians (both North, East and South India)
Funnily, over the years of my existence I am able to differentiate each of the ethnic traits be it Tamil, Punjabi, Gurajatis or any of the non-majority indian population.