I'm surprised there's so much skepticism about this – it seems like an intuitively obvious result. The date on which a child is born will influence the environment in which they spend the early months of their lives – levels of sunlight exposure, temperature, allergens, pesticides and so on, both for the child and the mother. Given that, and knowledge that exposure to certain environments and chemicals can change the risk of health conditions later in life, it's hardly a big leap to demonstrate that correlation through a larger population-scale study.

I'd be far more surprised if there were no link!