not sure if the derivation is correct. From my discussion with achow (https://bitcointalk.org/index.php?topic=1682183.msg21389041#msg21389041) I seem to understand, that segwit nodes send data in legacy format to "old" (non-segwit) nodes. This doesn't mean, the old client "get's nothing, and must trust". It still get's the data in old "legacy" format, and as such can decompose the tx inside, and verify the contents.
Further achow101 says: "all witness data stripped out" - I am not yet sure how to interpret this, does it mean that script sig(s) in the legacy format remain empty? That would mean, the legacy client is still able to verify tx contents, but spending is the difference.