I'm kind of wondering - maybe it's not actually the light. After all, that would be the most tenuous and feeble of connections. But of course even scientists have dreams and aspirations. ("Hey! Let's find a link between two things that's so tenuous and nebulous that it'll take us two page just to list the causal chain! THAT should get us a Nobel!")
But of course mostly that's not the way the world works, and the right link, when found, proves to be much more simple to explain and demonstrate. Occam's Razor dictates that we should plunk for the most simple explanation, and to me there's a much simpler explanation:
People who spend more time under artificial light are generally citizens of more developed countries, and are that portion of the population that spend their time awake for longer at night. That indicates a certain lifestyle, working long hours and getting recreational time in artificial light. A lifestyle that eats a lot more processed food and doesn't have the time for homecooked wholefoods... Or maybe they use more shampoo for some reason not directly linked to artificial light...
And it's easy to find a link between harmful diet and pretty much any cancer - more so than it would be to find a link between artificial light and cancer, I think. (I think even skin cancer, while caused by UV light, is facilitated more by harmful diet than by sunlight - don't forget that our forebears lived in broad daylight and full sunshine and there's no evidence to suggest that a skin cancer epidemic killed off as large a percentage of that population as it currently does of our generation.)