I'm a frequent car renter here in Costa Rica, and all of the car rental companies that I have used (Alamo, Avis, Economy, Sixt, Thrifty) do keep open vouchers with the carbon copy and raised numbers method. That voucher is for "unforeseen charges".
The deposit, rental, and coverage charges are processed through the electronic method (swipe).
I know it is a pain in the ***, but cars in Costa Rica are SO EXPENSIVE, that rental car companies want to cover themselves the best as they can, even for mini cars.