Another one to join the 'no' school of thought. The credit card is basic given as a guarantee - if you bring the car back damaged, without fuel when you were supposed to, or not at all! In my experience, they don't actually charge the card - they just take an imprint or the details just in case.
A debit card simply couldn't offer the same 'guarantee' - there is no way the hire company could know that you have sufficient funds in you account - I suppose the same is true of a credit card, but the likelihood is your credit limit is a lot higher than most of us have in our current accounts at any time (well me at least!).