The Marines would never take a man who had no use of his legs and had to be pushed in a wheel chair (FDR) either. By the time JFK was president, his back was so bad, he would be in agony for days. A number of presidents had ailments that would have made them unfit for Marine Corp service.
Mental or emotional ailments are an entirely different kettle of fish.
As I said, I an unsure where Migraines (if frequent and severe) fall on the spectrum, but this IS an issue.