AWR Hawkins with Breitbart News has this:
Breitbart News spoke with Crime Prevention Research Center president John Lott about the suggestion that a lack of information is allowing the wrong people to slip through our current background check system. Lott suggested the problem is completely different—that the real problem is in how our current background check system can inadvertently prevent law-abiding citizens from getting the guns they need when they need them.
According to Lott:
Virtually the only people who are stopped from buying guns by the current background check system are law-abiding citizens who were mistakenly prevented from buying a gun. If the background check system is missing a few names, it really only means that there will be fewer false positive cases where law-abiding citizens are stopped from buying a gun because they have a name that is similar to someone that the government really wanted to stop. Mistakes that prevent some law-abiding citizens from quickly getting guns when needed for protection cause real harm to people’s safety and this needs to be acknowledged.
With almost all those denied purchases of guns being false positives, adding more names to the systems will primarily result in more false positives. There is no discussion of trying to fix these problems.
See also guns.com for a similar discussion.