OK boys and girls.
Licensed vehicles are not subject to local sales tax but are taxed under the use tax rules and regulations. The tax is remitted to the jurisdiction where the vehicle is licensed,...ie: used.
Dealers with nearby different use tax collection agencies will register with those taxing bodies to collect and remit to the appropriate taxing agency.
State border communities will do this as expected customer service. Nobody in central Iowa, for example, will collect and remit Illinois use tax for a customer from Moline, IL. That customer will pay the tax when the vehicle is licensed in Rock Island county.
BTW, notice how vehicles are not subject to local option SALES tax. Only subject to use tax rules and reg's.