Hexidismal--
You've got it right: you should not sell to anyone who you think would be unsafe.
The fact that you've volunteered to train this guy at the range is good, not just for him but to give you more info on how he acts with guns. Maybe you'll find he is indeed safe; if not, then don't sell (Lawyer: "So, you felt my client was SO likely to injure himself with your deadly assault weapon that you posted that fact ON THE INTERNET, but now you say your not RESPONSIBLE for the fact that he is in fact now injured, just as you KNEW would happen?").
I'm pretty chatty with a couple of the FFLs in my area, and they ALL have stories about times they decided not to sell. Most of them are funny, but a lot make your neck hairs stand.
It hurts ALL gunowners when someone who's irresponsible gets hold of a gun, so it IS our responsibility to discourage that ('cause if not, we'll pay the price.) Huge difference between the gov't saying, "You can't buy! Peroid!" and a private citizen saying, "I won't sell. To you. My choice."
For MinnMooney--
Buying with intention to gift the firearm is a strawman purchase? I guess a lot of father-sons, father-daughters (and my own mom--thanks for the .357, Mom!) are headed to jail. (By the day, my mom didn't run a background check on me on my birthday--another loophole!!!!!!!!!! Where's John McCain?) Please don't give any anti-gun police depts (or the BATFE!) new ideas!
Purchasing for someone who COULD NOT purchase for themselves (felon, unlicensed, etc.) is illegal. See BATFE's webite: "Purchase a gun for someone who can't [legally, not financially] and buy yourself 10 years in jail." (Bad enough when the police don't know the law--gunnies really should.)