But wasn't there recent news about the NRA having their own database?
Yes, but that is not a problem because they are not the goverment.
There is this strange belief in USA that anything connected to the goverment is evil and apparently as an extension of that belief the opposite is also true. So just because the 2nd amendmend fundies have raged against any data concerning who in USA owns guns BY THE GOVERMENT, they have no problems with NRA having such files and in fact violating several laws by having such files.
Because even though goverment having such a list would automatically mean it will be misused there is no possibility of an independent organisation misusing such a list...
It's not a very precise of sound logic, I know. I mean they hate the goverment spying on people but don't mind corporations doing so. On the other hand they didn't mind goverment torturing people even though they would have had a perfect opportunity in privatizing Guantanamo Bay prison and turning over the torture to some corporation. (which according to MURRICA logic should have made it more efficient and cheaper than the public option.)