In Florida I've seen both. The way I read it, they shouldn't collect sales tax on a transfer.
IMO, I wouldn't worry about it on the state level. The state of Florida won't doesn't do regular audits unless it's a business like a car dealership that does a high volume of sales tax. They figured out it cost more to enforce it than they were recovering in unpaid taxes. A gun shop isn't going to get audited unless there's a complaint.
The only way I could see it being an issue is if the ATF decided you weren't complying with state law and revoked a FFL. IMO, the dealers here who are collecting sales tax on transfers are doing it because they're overly cautious. Of course, the state isn't too concerned with people collecting more tax than they're supposed to, just concerned with people collected less tax. I see convenience stores collecting tax on over the counter drugs. It's clear cut, but try reporting it to our DOR.
In any case, there isn't a requirement for a dealer or a private party to send an invoice to your FFL. So how does he know what you paid for the gun? If you paid for the gun. What if it was a gift? Or bartered? Or inherited? He's not a party to the money changing hands.
He's not doing the sale. He's handling a transfer of title. Not even that. He's handling a transfer of possession between two parties. No sale.