We should have access but really, the list should probably not even exist as it is. They dont prosecute those who willfully break the law attempting to buy something they are not entitled to by law. Nobody involved in the NICS system has a damn thing at stake in this other than having to correct it at some point if you can prove to them your not guilty of something they erroneously report.
Any level of failure to deliver on our rights is not acceptable to me. Is it ever OK to deny a citizen Free Speech? We should be able to see our NICS report but I would be a bigger fan of doing away with it altogether.