Basically what you've recounted is what I've heard, with slight differences.
Looks like NYT had an article on this, even:
About a decade ago I had several friend from all over the subcontinent; I worked, I'll just say, "in computers." (Not a big fan of detailing explicit personal histories on this forum.) After a few months of regular lunching, after work get-togethers, etc., I was surprised to learn the amazing degree of complexity, nuance, and the like, between not only the various regions and dialects within India, but how Indian folks related to and clashed with Bangladeshis and Pakistanis. Though the Pakistani folks I knew were Muslim like the Bengalis, my Bengali pals preferred to hang out with the Indians, who were all Hindu; and I learned all about the decades-old bad blood having to do with the wars of secession -- Pakistan's declaration of war on Bangladesh, for ex., which India put a stop to.
(Chomsky has noted that India's putting a halt to Pakistan's aggression against Bangladesh is a "humanitarian intervention" you never hear of, because it's the wrong country that would get the credit -- India. And only the USA is supposed to get credit for humanely intervening in conflicts.) There was lots more, but way too much to go into here. I think the subcontinent is a fascinating place, and not just because the food is awesome!
-B.
Andy F wrote:
"I wonder if there's a bit of northern/southern Indian history in this. It was once explained to me that southern Indians (such as Tamils) had been driven south way back when by the Aryan (are they still called that?) cultures, and that the ethnic southerns tended from the outset to be darker skinned than the northern invaders -- they show up as those blue-skinned people in old Indian paintings. I imagine the lighter-skinned Mugals who came and conquered later would have added to light-skinned status ."