I got some information today from my accountant regarding under what circumstances the Tax Office demand documents with an Apostille Stamp. Generally if you are tax resident in Greece and you are declaring an income as taxable in Greece then they will usually accept a certificate of that income without an Apostille Stamp. If, however, you are declaring an income as NOT taxable in Greece, e.g. because of a Double Taxation Agreement, they they will usually demand that the income is supported with a certificate with an Apostille Stamp.
Obviously this is not guaranteed, since the tax office do whatever they feel like on the day, but it might help to understand when the Tax Office are likely to ask for an Apostille Stamp.