From what I see Florida doesn't use NICS to process transactions, they use a State resource called FDLE. The exception is pawnbrokers redeeming pawned firearms. So the NRA is just flat wrong there. In Florida a concealed carry license doesn't exempt you from the purchase background check, but there are several states where it does.
It's confusing, but if the NRA can't get it right it's not surprising a reporter got it wrong. It's entirely possible one of those 365 individuals could have (and probably did) purchase a firearm.
FDLE - FAQs1
https://www.atf.gov/rules-and-regulations/permanent-brady-state-lists
https://www.atf.gov/rules-and-regulations/permanent-brady-permit-chart
It's confusing, but if the NRA can't get it right it's not surprising a reporter got it wrong. It's entirely possible one of those 365 individuals could have (and probably did) purchase a firearm.
FDLE - FAQs1
https://www.atf.gov/rules-and-regulations/permanent-brady-state-lists
https://www.atf.gov/rules-and-regulations/permanent-brady-permit-chart