Anyone complaining about αρχαίο—παλιό needs to give the Greeks their due. When you have a continuous civilization of 3,000 years and any day could bring the excavation of a 3,000 year old treasure trove in your back yard (as happened at Pylos recently—today is January 2017), you get to have lots of words for old(en)!
The Olympic games started in 776 BC. According to you Greece would have been only circa 250 years old then if Greece is 3000 years old as you wrote. So I am supposed to believe Greece was only 250 years old then. Not. They recently discovered human footprints in clay that changed to stone on Crete dating back 5 million years.