There are some misconceptions being repeated here, along with some truth. It does appear that the law tells FFL dealers they can only run the check (phone call) if you are buying a gun. However, failing the instant check does not automatically mean you are a prohibited person.
As was noted, there are many things that can give you a "delayed", or even a "denied" response, without you being a prohibited person. That's why there is an appeals process. I know one individual who got delayed, because his file was flagged. He was not a prohibited person. Yet his file was flagged. The official on the other end of the phone doesn't know why a file is flagged, only if it is, or not. The details get resolved in the appeals process. As it turned out, my friend with the flagged file had been flagged because he had a govt. security clearance! He did get his gun, and got the "flag" issue resolved as well.
I'm no lawyer, and don't claim to be, but I am under the impression that if the sale is denied, the dealer MUST return ALL the money you give him. Ethically, he has to give you either your money, or the gun. Anything else is fraud. I have bought a number of guns from dealers over the years, and never had a single one of them even ring up the sale before making the phone call.
Apply for a concealed weapon permit and you will know if you would have a problem buying. If you get the permit then background checks are not required every time you buy a gun.
Incorrect. Getting a permit will tell you that you are not a prohibited person, but it does not get you out of the dealer making the instant check phone call. That is the dealer's responsibility, and must be done for every purchase, every time, no matter what kind of permit you have. What a permit may get you out of (depending on individual state law) is the waiting period. The Brady law required a waiting period for handguns (so a background check could be done). This was a Federal law, and independent of state law. If your state required a waiting period, it could be concurrent with the Brady law waiting period. The deal struck by the NRA and the Feds was that when the instant check became possible (which it wasn't when the law was passed), in exchange for dropping the waiting period, the instant check (phone call) would be done for all firearms, not just handguns.
Which is what we have today. Individual states, which had waiting periods for handguns, before the Brady Law, kept them. I live in a state with a waiting period for handguns. 3 business days, the last time I checked. Totally independent of Federal law. However, my state also says that if you have a CPL, the waiting period is waived. Again, totally independent of Fed Law. Different states have different laws.
So, If I buy a handgun from a dealer, I fill out the fed forms, dealer makes the fed phone call, and with my state CPL permit, I pay the dealer, and walk out with the gun. Without the state CPL, the exact same thing happens, except I don't get to walk out with the gun, I come back in 3 days and pick it up.
NO state permit waives the Fed background check phone call.