When a gun that was purchased without a background check is used in a crime, it is "proof" that all transfers must be made with the check.
When a gun is used in a crime that was obtained with a check, but was otherwise unregistered or unlicensed it is "proof" that all guns need registration and/or licensing.
And when a registered, background-checked gun is used in a crime, it's proof that that particular type of gun (handgun, "assault weapon," "junk" gun, etc.) needs to be banned.
There is no level of governmental control or restriction that is sufficient for them, such that when that level of control is reached, the focus is no longer on additional restrictions. Since pushes for more control will always come, it is vital to always resist them.
Absolutely. Gun control isn't about guns, it's about control. We will ignore that at our peril.