TN's carry permit does not get you a quick pass on the background check.
IIRC, that loophole is only good if the state issuing the permit does regular (annual, I believe) background checks of carry permit holders. TN only does the background check when the permit is renewed, so we don't qualify.
Additionally, TN is one of the limited number of states which uses their own instant check system, through TBI, rather than the FBI's. As such, the state is allowed by statute to charge up to $14 per background check. TN charges $10 per.
If TN Department of Safety and Homeland Security did annual checks on all permit holders to allow us to bypass the background check when transfering a gun, it would increase workload and, inevitabley, cost, for that department while there would be fewer background checks run through TBI, which would result in less income for that agency.