Join Date: May 2000
Location: Houston, TX, USA
Programs: UA 1K, AA Lifetime Platinum, DL Platinum, Honors Diamond, Bonvoy Titanium, Hertz Platinum
Posts: 7,969
As others have mosted, most US car rental agencies require a non-debit credit card at time of rental, although a debit card may be used at the end of the rental to settle the charges.
I question whether a car rental agency would be able to tell that a MasterCard/Visa from Europe was a debit or a credit card. Maybe I'm wrong, but I've just assumed that this was determined by knowing the unique card number prefixes used by US banks for debit cards, rather than anything that goes on real-time during the authorization process.