Seems that there is some confusion about some acronyms (CCW, NICS,...), from the ATF website:
View attachment 8510732
Point #1 - a CCW license falls under a state permit. The things that would cancel or prevent a CCW would cause a flag during a NICS
Going back to the OPs comment about a cop being able to see what guns you own - I would guess if there is a state registry the cops have access. If there is no state registry then there is not "gun list" for the cop to check.