I believe it did make it to the Greeks; but not the Romans, who rather choose to focus on the self-mutilations aspect, as well as her Gallus performing castration rites and practicing transgenderism... a fact that Martin Luther would latch onto and equate the performance of current Christian clergy seemed to emulate by practicing celibacy.In the Phrygian archetype, She was believed of having taken the form of a stone of black meteoric iron, a belief that wans't as far as I can recall mantained during her "migration" to the Greek and later Roman pantheon. That is what I was alluding when I said that it tied nicely with the turning to stone motif of the Demonothan. I might be wrong though, haven't read on the subject on a long time.
In fact, even here in the states you will sometimes still see a pine cone at the entrance of some homes, either carved in the stone or included in a wreath... though, I am sure that many do not understand the reference of such things.