Correct. Because they don't look into it, nor require a medical exam like aviation does, and there isn't any justification to begin doing so as far as special weapons are concerned. The whole aviation medical process is over the top for purposes of private flying.
The point is that the Feds don't spend all the effort looking into one's mental health for weapon ownership that they do for flying. Several reasons come to mind.
1) Different origins. FAA medicals had their birth in military flight physicals. Owning arms has been around a bit longer and predates modern medicine.
2) Keeping arms is a right guaranteed by the Consitution and has a much higher threshold for limitations than flying. Flying an airplane is not a right protected by the Constitution.
3) There's very little history of people killing other people with things like mortars, outside a war. Airplane deaths are much more common. (And frankly, there's scant evidence to indicate a class 3 medical prevents aviation fatalities.)
