I believe the issue is private sellers. Some states require that if you want to sell a firearm you have to broker it through a firearms dealer who can run the paperwork and background checks. These same states require that the physical part of an internet transaction also takes place at a firearms dealer - so I can buy a gun on the internet, but it would be shipped to the local firearms dealer for me to pick up, and do all the required paperwork before I can take possession.

In states that do not require a firearms broker then firearms can be transferred without government knowledge. I believe some of the arguments for not requiring the transfer revolve around familial transfers and inheritance - why should I have to pay someone to take ownership of my grandfathers gun collection - type of thing. But that just allows free sale of firearms on a street corner to any unsavory customer with sufficient coinage.

The way to go is to provide access to a cheap (and it needs to be cheap or free, because cost can and will discourage its use) national background check and registry, that private sellers can access. But that still does not get around criminal sales, and fraudulent claims by the buyer. I have no way to prove 100% that the person in front of me is who they claim they are.
I used to think it was terrible that life was unfair. Then I thought what if life were fair and all of the terrible things that happen came because we really deserved them? Now I take comfort in the general unfairness and hostility of the universe.