My sister works reservations at Enterprise, which also reserves for National and Alamo. They are told to disclose that they do not take debit cards. As others have said however, every company is different, and many have different policies depending on which counter you are at and in which state.

If the person you spoke to said there would be a credit check, believe them. That doesn't mean an agent won't do it if they are busy, or aren't following procedure. Just don't count on it.

Some of the others posting may have an account/history/status with a particular company or even one thru a business, and yes, you are treated differently. The easiest thing for your client would be to get a pre-paid credit card, they are open to just about anyone.