Some do, but most do not. Some will require a credit check first, as anybody can get a debit card, but they assume not everybody can get a credit card.

It's harder to enforce a hold on a debit card (if not impossible), people don't like the fact it could be weeks before the hold comes off of the debit cards, so there's lots of customer service issues there, so it's just easier for them not to deal with it.

Hertz does accept debit cards at many locations, but of course that significantly depends on the local policy at that location.

Many will require additional restrictions (you need to pass a credit check, they put a larger hold on the card, they require you to take out the insurance, etc)

Can I use my Debit Card or Bank Card to reserve a Hertz car?

At most Hertz locations, debit cards (sometimes called check cards) issued under a VISA or Mastercard logo which draw funds directly from the cardholder's account may be used to qualify for rental. However, prepaid or stored value cards which have a VISA or Mastercard logo are not accepted to qualify for rental. Debit cards must have available funds for the estimated amount of the rental charges plus up to $140 to cover any incidental charges in order to secure the rental. Both debit cards and prepaid or stored value cards issued under a VISA or Mastercard logo may be used as a form of payment when you return the vehicle. Please contact your local Hertz Reservations Office if you have a question about whether Hertz will accept a certain card.