Although several clinical studies focused on the health effects of CBD, the results available so far were not enough to convince the FDA to approve it as a drug. The FDA does not agree with its use as a dietary supplement either, but as long as sellers publish the appropriate disclaimers (like those on the CBDPure website and labels), it’s not up to them.
Pharmacology published a study in 2016 looking at medical marijuana for migraines, specifically in relation to its effects on serotonin, with very positive results. You’ll notice that neither study looked at CBD in isolation from other cannabinoids (which is an issue with a lot of research on CBD and pain). Truthfully, the research on CBD alone just isn’t sufficient to make any pronouncements about its effects on headache pain.