Well, most migraine triggers are basically oxidative stress (https://onlinelibrary.wiley.com/doi/abs/10.1111/head.12725), and it is impossible to avoid oxidative stress since even simply burning glucose contributes to it.
Honestly, I've long dismissed the claimed benefits of ketogenic diets like 'reduced inflamation' as... minor and uninteresting. A few weeks into a low-carb diet for my migraines and my sedentary butt is suddenly running and with my untrained knees never having felt better. I would not be shocked if there were other beneficial effects of ketosis on migraines.