There are two taxes when purchasing a vehicle: property tax with the county treasurer’s office and sales tax with the SC Department of Motor Vehicles.
The dealership is allowed to pick up your tags on a vehicle without paying local property taxes. When the dealer states that they are taking care of your taxes, they are referring to sales tax, which is paid to the Department of Motor Vehicles, not your property tax paid to the Treasurer’s Office. This allows you a 120-day grace period to delay payment of personal property taxes on your new vehicle.