Yes, Greece is one of the signatory countries in the Hague Convention of October 5, 1961, and as such, all documents that bear the Apostille seal are legal and valid to be used by Greek authorities. They do not need to be stamped by the Consulate.
I was told I need to go to the Consulate or the Embassy for certification of documents for Greece
There is no need to go to the Consulate or the Embassy to certify documents to be used in Greece. The Apostille stamp/certification is all that is needed.