No, Nutella would be too dark. To attain a tan bebe, you have to eat halwa, chai with milk, and brown rice. Eat haleem to get tan-skinned baby with yellow undertones.
More seriously though, milk is applied topically to the skin for its exfoliating and mild bleaching effects as it contains lactic acid. So, perhaps the “milk=fair child” theory arose from this topical observation of milk and maybe the belief that it would have greater impact on the developing baby’s skin as it’s more delicate/ more penetrable. Just a guess.