Can you legally sell a vehicle without a clean title at time of purchase in State of Florida?

II bought a 2006 Cadilac DTS by paying $2,865.00 ($2500 for vehicle and $365.00 for title, sales tax, and transfer of tag) in cash on 8/10/2020. At time of sale, the car lot "never disclosed it had a rebuit title or it needed to be inspected at time of purchase. Nor would I have bought this vehicle had I be informed of this. I wasn't aware until September 8, 2020 when I tried to get the paoer title from Florida DMV so I can sell this vehicle and was told by DMV "there was never no title filed in State of Florida and that the 2006 Cadilac DTS was legally registered in my name based on the VIN # on bill of sale. I immediately contacted the car lot where i bought this vehicle when they told me "the car needs to be inspected by Florida DMV "before the transfer of the title will be in my name. I immediately requested a "full refund of all monies paid and the car lot stated "they will buy the vehicle back but never did". Lot illegally seized this vehicle and won't refund money I paid cash.