According to the Convention on Road Traffic European law only European driving license and the countries that have signed the Vienna Convention are allowed to drive in Greece below are the countries that can drive in Greece
Albania, Armenia, Austria, Azerbaijan, Bahamas, Bahrain, Belarus, Belgium, Bosnia & Herzegovina, Brazil, Bulgaria, Central African Republic, Chile, Costa Rica, Cote d’ Ivoire, Croatia, Cuba, Czech Republic, Cyprus, Democratic Republic of Congo, Denmark, Ecuador, Estonia, Finland, France, Georgia, Germany, Ghana, Guyana, Holy See, Hungary, Iceland, Indonesia, Iraq, Iran, Ireland, Israel, Italy, Kazakhstan, Kenya, Kuwait, Kyrgyzstan, Latvia, Liberia, Lichtenstein, Lithuania, Luxembourg, Malta, Mexico, Monaco, Mongolia, Montenegro, Morocco, Netherlands, Niger, Norway, Pakistan, Peru, Philippines, Poland, Portugal, Qatar, Republic of Korea, Republic of Moldova, Romania, Russian Federation, San Marino, Saudi Arabia, Senegal, Serbia, Seychelles, Slovakia, Slovenia, South Africa, Spain, Sweden, Switzerland, Tajikistan, Thailand, The former Yugoslav Rep. of Macedonia, Tunisia, Turkey, Turkmenistan, Ukraine, United Arab Emirates, UK of Great Britain & Northern Ireland, Uruguay, Uzbekistan, Venezuela, Vietnam, Zimbabwe.
This is a link with the the Convention
In a case that you risk to rent a car without the appropriate documents you run the risk of 1000,00 € fine to the driver and 1000,00 € fine to the car hire agent and confiscating the car.
In case of an accident the client is running the risk of begging uncovered by the insurance company.