See question 11f.
He could have legally purchased a gun.
Even if the answer to 11f was yes, all he had to do is lie and no one would be the wiser since he is protected by HIPPA laws that won’t let his doctor disclose that information.
http://www.atf.gov/forms/download/atf-f-4473-1.pdf
The FBI does background checks. His condition would have been exposed.