"Legally" - NO. You understand incorrectly.
Illegally - Yes. He can lie his ass off to a 'private party' like he did at the Gun Store.
In addition, here in IL if I sell one of the guns in my collection to a private party he has to have an IL FOID Card. Now if he just got released from a loony bin last week I'd have no way of knowing. His FOID Card would still be 'valid' (in appearance).
And what's with the NRA slam??
It seems to me that anyone buying a gun should be subject to background checks. If you buy it from a private party, the same precautions should apply.
Who put this loophole in the law?