Putting a charge through to visa if you damage the car is more reliable than trying to charge a debit card. In the US people without credit cards often have poor credit, often from not paying back debts (or so goes the stigma), and I'm not sure if you can just charge more to a debit card later (it's been a while since I've used one).

Plus, then if you can't pay, it's visa's problem, not theirs.