In the case of my husband, as explained above, thank goodness they "just let him go" because it was their records at fault, not my husband trying to do something illegal.
The person making the call (merchant) for the background check is not told why someone is rejected - they are just told yes or no. So unless the LEO who knows why there is a rejection being made either tells the merchant to stall the "purchaser" or just delays giving an answer until a unit can be dispatched to the location the rejected would-be purchaser would be free to leave.
There have been 2 examples on this thread of people being denied, neither of whom were attempting to illegally purchase a firearm. I'm sure there a thousands of similar stories..
While the original intent of background checks may have had some good intentions - the system is terribly, terribly flawed.