I want to know how they would know if you'd been in a mental facility or rehab?
Those are private records, and they can't get those accessed.

Even if you've been taken to court, and labeled mentally ill, it doesn't show like if you have a parking ticket, or other "law problem"..

So.. buying a gun for say hunting.. not an issue.
Buying a gun for say.. suicide.. well.. I'd hope you'd not get that far.