Actually, IME, most rental offices only carry the US version of the "big book of driver's licenses." For international ones, especially ones that aren't printed in Latin text, they rely on the customer providing an International Driving Permit to verify the validity of (and translate the information on) the actual license.

You may want to go get an IDP. Having one will likely make your case that your license is valid much stronger. You can't get an IDP without showing your real driver's license to the entity issuing the IDP, so you can make the argument to Avis that the agency you got the IDP from verified that your driver's license is valid and should thus be accepted by Avis.