The researchers in the Nature article compared blind people with migraines with normal-sighted people also suffering regular migraines, who had been matched on age, age of onset (most started around age 17 to 18, give or take several years), occurrence of an aura and other medical factors. They found that only the blind people with an intact optic nerve had their migraine exacerbated by light, along with the seeing people. The blind people whose optic nerves were still Okay (ie. they could transmit information to the brain about light vs. dark, but not about lines, shapes and colours) had their migraines made worse whereas the blind people without optic nerves and/or no eyeballs did not.
The authors give really detailed information for the knowledgeable about the nerve pathways involved, but I won't go into any of that. I think the fact that the study appeared in such a prestigious scientific publication is good evidence that the research is quite sound and migraineurs can be assured they're not crying wolf!