Two entirely different checks. One, done by the police was a background check of YOU. The other was a cross reference check against a list of people. The list probably doesn't have YOU on it. Rather, as Yancer said, it has a lot of people that look like you.
I've had the same thing happen. Not a denial. Just not an immediate approval. The FFL couldn't transfer it right then and there. But he could in 5 days. He didn't even have to call back in 5 days.
Therein lies the whole problem with the BS national data base. Just like the "No fly" list, it is wrought with errors. I don't really have a problem with a real background check done on ME. But I do have a problem with comparing me to a list of a whole bunch that might look like ME.