This statement is quite misleading. Regardless, of where the guns were purchased the overwhelming majority were stolen by either the shooter or someone else who illegally sold it to the shooter. I also note that the places with these supposedly "lax gun laws" don't have near the shooting that Chicago has, so it's not the laws of these states that is the problem.
The only way you can buy a gun on the internet without a background check is to buy it from someone like Trayvon Martin.
It's a Federal law that covers all states that all sales through licensed dealers must conduct a NICS background check.