I agree with vasnTearn on this.
We do not speak of one nature, but of one incarnate nature and one incarnate hypostasis.
The Word is indeed one nature and one hypostasis, but one nature and one hypostasis who has become incarnate.
As St Cyril says of those who opposed his Orthodox Christology,
Again they twist the facts, failing to recognize that the reality is one incarnate nature of the Word.... he displayed to us one nature, but as I said 'one incarnate nature', of the Son.
It was Nestorius who said,
You should not accuse me as if I did not confess a single person in two natures..
Whatever either meant by these terms it is clear that to those who followed St Cyril, the proposition that Christ was a single person in two natures was an entirely Nestorian terminology.