If you have reason to believe that the buyer is a felon you can't make the sale, but I can see a agent reading a C&R for selling a gun to a guy that had warrants or previous convictions.
Like you said, FFL03s have no way to do a background check, so how would one have any reason to think the buyer is a felon unless he/she told you so? The best that can be done is to look at ID to verify age and address, and take his/her word that they can legally buy and own the gun. Personally, I wouldn't (and don't) sell guns (either C&R or non) to someone I don't personally know and trust, or to someone that can't be vouched for in some way by someone I do know and trust, but if a BATFE agent called on me and said a gun that I used to have in my collection was then used in a felony, I would show him my book and let him continue his investigation. I don't think I'd stand for him chastising or threatening me, in any way, when I did everything in my capability to ensure that the deal was legal.