If it's a handgun, I won't sell it to/through anyone except a licensed dealer, even if it's to someone I know, because who knows who that person might sell to, who then might sell it to, etc... Loosing a $100 or whatever less a dealer will give you for it, is worth it.
For rifle FTF transactions, I always write down the name in my records, and an address and/or phone number, etc. With all the databases available to LE these days, it doesn't take much specific information for them to find someone. I just sold a rifle FTF to someone at the fun show yesterday. Before I even left the fun show, I Googled his name from my iPhone, and got a picture of him from his face book account!
I can understand buyers not wanting to give up a copy of their driver's license these days, with all the identity theft, etc, going on. Having a copy of someone's driver's license is almost as good as having a credit card in their name.