This is a really bizarre interpretation, considering that the 'writing of ancient Greece' was only endangered due the destruction of the eastern Roman Empire (and the Persian Empire) by the Muslim conquests. The era of the conquests was extremely chaotic and a major setback for civilization in the region. The historical record practically falls apart because of this. Prior to the conquests, the eastern Roman Empire and its long heritage of learning and culture was trucking along quite happily, even if there were periodic border conflicts with the Persians.
Even during the conquests and their ever-shrinking territory, the Romans maintained their technological superiority over the surrounding civilizations. The final conquest of Constantinople, and the consequent fleeing of the learned with their texts westward, was a key factor in helping along the European Renaissance.
It's always been a bit strange to me how the history of the Roman Empire is pretty much ignored after the fall of the western empire. The East remained one of the greatest, wealthiest, and most educated powers in the world for centuries.