My understanding, though, is that Persian society, having been heavily influenced earlier on by Hellenic culture, pretty much sequestered their women away - just as Arab society does today, but back in Mohammad's time, it didn't.
Let's not be naive. The Persian Empire controlled various parts of Hellanic culture for hundreds of years, so more than likely a large majority of philosphical and political advancements came from the Persians and not from the Greeks. In fact, this is something that virtually every single one of my Greek friends admits to, as did Aristotle, and Alexander the Great.