If A sends a coin to B, then the commitment is separate from the signature and the transaction. If B later sends that coin to C, then B does need to include A’s commitment into the TX; this part was omitted from the earlier description.
If A sends a coin to B, then the commitment is separate from the signature and the transaction. If B later sends that coin to C, then B does need to include A’s commitment into the TX; this part was omitted from the earlier description.