What a mess!
I've witnessed people get denied by NICS for some real silly reasons. And it is up the person denied to prove their/NICS's mistake. This can take months or years.
I knew someone that had to get the State police involved.. the sheriff, and his congress rep just to have his 'confirmed denial' overturned. During this whole process, he applied for his CCW permit and was approved by the State police - that run the same federal check.