They definitely do though - all big brands like Avis, Europcar, Hertz will refuse a Visa Debit card, it has to be a Credit card - I always have to use smaller local rental companies which are willing to take a risk on a debit card. At least that has been my experience renting around Europe.
I still don't use a credit card for that. I have a debit card that's part of Visa, so most businesses don't care whether it's debit or credit.