Correct me if I'm wrong, but it's still possible to double spend the transcripted coin?

1. Alice sends Bob the using the off-chain system.
2. She also redeems it onto the chain. She can do this anytime before Bob does (or whoever he passes it on to).

Or is the idea that redemption step still requires the participation of the offchain system?
If so it's still superior to existing off-chain systems in that funds can only be frozen, not confiscated.