"Now the full tracking of a firearm to the last owner is flawed because of private sales do not require paperwork"

Aren't the sellers required to phone the FBI and other agencies to ensure the buyer doesn't have a criminal record and is fit to buy the gun? This is how they know how many guns are sold (legally) in the US. This was reported in a UK broadsheet but I can't find the reference for love nor money; apparently there have been millions of guns sold in 2012 already.