Hertz, and other rental car companies, have some strange policies when it comes to debit cards. In Hertz's case, the credit check and $200 incidental deposit (it should be returned at the end of the rental if there are no incidental charges) are required when using a branded Visa or Mastercad debit card.
I agree that I would not want my credit report pulled for something as singular as a car rental. But please understand this is Hertz's policy, not AAA's. Other rental companies may have similar policies.