OK, I've done the reading as @johnyj suggested, as I now understand it: a non-segwit transaction includes the signature to create the txid. A segwit transaction does not include the signature. That's why the signature can be safely trimmed and why it is a fix for transaction malleability.If signature data is removed, there is no way to calculate the TXID for each transaction
[doublepost=1459420364][/doublepost]Also my understanding is now that when a segwit transaction has been sent to a non-upgraded wallet's address, that wallet cannot see it and it will not show up unconfirmed (as a non-segwit transaction would do). Once that segwit transaction is included in a block, it will show up in the wallet and can then be spent.
i.e. non-upgraded wallets WILL be able to spend segwit transacted coins.