You have a name and birthday same as a convicted felon. You get a denial. You decide to appeal with FBI, which takes forever. In the meantime you buy a firearm in a private sale, and you keep the other 25 that you already have and shoot them. Should the ATF kick down your door and take the guns? Why? You're not prohibited. But they may kill your dog and throw a flashbang in your house at midnight and then shoot you when you try to defend yourself with you legally possessed guns.
Or even closer to the scenario being discussed...you get a delay, it lasts longer than 3 business days, the FFL does the transfer and you take your gun home. Later the FBI decides you're prohibited (you are not), and tells ATF to go get your gun. So how do they go about retrieving the gun? The proper way would be to investigate whether the denial was legitimate, perhaps by talking to you, the FFL, and the FBI. If ATF has enough probable cause to believe that you're prohibited (remember, you're not), they take it to a federal magistrate for a warrant to search your house or person for the gun and retrieve it, to be used as potential evidence in a case of illegal purchase/possession of a firearm (which they will ultimately lose).
Now you see that investigating the all the NICS denials may not be as exciting as making other cases and why it may not be a high priority for ATF. There are probably thousands of "false positive" denials per year and the denials need to be thoroughly investigated in order to make a criminal case. In fact, this is one of the reasons why illegal possession cases are rarely investigated or made by Federal law enforcement. They don't want to waste their time, just like the DEA won't waste their time making a simple possession case on 1/4 oz of weed in Colorado.
The other issue of the NICS system is that it can theoretically be used to deny purchase to non-prohibited persons. It is possible to get a denial in NICS if you are an "unlawful user" of illegal drugs. But this is not a prohibiting factor in your ownership. So if you were to lie or make an error on 4473 and get a firearm when you are an unlawful user of drugs...the appropriate crime to be charged would be lying on the 4473. Same for straw purchase for a non-prohibited individual.
There's lots of people lining up to make NICS (that's YOU, Sen. Cornyn) into a bigger overreach and denial of rights. Oh you took Duloxotine (Cymbalta) for nerve pain? You are adjudicated mentally defective, no guns for you. Chantix to quit smoking? That's a SSRI, you must be bipolar. Had a hard time when you came back from Iraq, you're PTSD, no guns for you.
