"Show me just what Mohammed brought that was new, and there you will find things only evil and inhuman, such as his command to spread by the sword the faith he preached." - Manuel II Palelologus
That's generally true, but not always. When I was an FFL dealer in the early '90s I heard of applicants in that area who were turned down at other FFL dealers by the instant background check (which BTW was anything but instant in those early days of the system) because of a criminal record or a falsified yellow sheet application.
I never heard of BATF or any LE agency investigating those falsified 4473 forms, which led me to believe that prosecution in those cases may be more threat than reality, at least back at that time.