One of the reasons I have a CCW permit is because, although you still fill out the form 4473, the background check is not run ..... at least this is how it works in AZ. Moreover I will not purchase a gun if the form 4473 is computerized.... ie you enter your info into an online 4473 system vs a paper form 4473.
Sure, the FFL has the paper form 4473, but the Fed's would have to scour a whole bunch of paper form 4473's to get a look at what I have acquired.
Works the same way in Nebraska. But you are living in a fantasy world. Your background check is run every 5 years on renewal of the CCW under Federal law to keep the Brady exemption.
Your biggest fantasy is thinking that you are safe. You’ve already given them a mugshot, fingerprints, DL# and home address which must be current to keep your CCW. They know who and where you are and the fact you have a CCW so you are a gun owner/buyer.