Anyone who is in the business of buying and selling guns must, by law, be a registered gun dealer. Registered gun dealers are required, by law, to conduct a background check on those they sell guns to (even if they make that sale at a gun show). This information is in the link which you presented above. On the other hand, private sellers (that would be people who have decided that they have more guns than they need and want to sell a few of them, or people who inherited a gun collection from their parents and want to sell them) are not required to conduct a background check. As a matter of fact, private sellers are not able to conduct a background check (you must be a licensed firearms dealer to have access to the background check database) and none of the "universal background check" laws propose giving private sellers access to that database. Those proposed laws propose forcing all gun sales to go through a licensed dealer. A likely result of "universal" background checks will be that it won't be worth their while to sell the guns for someone who inherits them. Rather they will just give them away (or "throw them away" if the law does not allow them to be given away). If that were to happen, it would be a bonanza for criminals.