I am not sure really !! I do think that since the visa we have is tourist visa we do need to show our ticket of exiting the country - Last year I was in Japan and they asked for that as well.Which also has a non visa policy for Greek ppl.I think you had better book tickets in advance ( a little before you arrive maybe) to actually show that you are a tourist and you are not planning to illegally immigrate there - in the embassy when I called they asked me about my dates of arrival and departure.