Because you don't apply to a gun company to buy a gun. (You actually apply to the government...chew on that one for a while.)
The government isn't attesting to your capabilities - that is still on you as a citizen.
>... background check
Who requires these background checks? Because the seller wouldn't do them unless obligated. Obviously the check and paperwork around it constitutes at least a de facto application to the government for permission to purchase the firearm.