Yep you are correct! asked my father who clarified it for me. However, Greece's "registration" tax really is ridiculously high!
With regards to buying a car in Athens, you are free to do that and keep it wherever you wish in Greece as MartynG states. Just like in the UK, I can buy a car in Glasgow and drive it to London where I live.
However, buying an automatic car; especially a small one is nigh on impossible in Greece. For some reason (again may be a Government thing)automatics are very rare! Believe me, if you can, just buy a small call with a standard gearbox!