In the Lightning Network Paper (https://lightning.network/lightning-network-paper.pdf), Breach Remedy Transactions seem to require signatures by both channel members. I infer this from this description in the paper:
When a new pair of Commitment Transactions (C2a/C2b) is agreed upon, both parties will sign and exchange signatures for the new Commit- ment Transaction, then invalidate the old Commitment Transaction. This invalidation occurs by having both parties sign a Breach Remedy Trans- action (BR1), which supersedes the Revocable Delivery Transaction (RD1). Each party hands to the other a half-signed revocation (BR1) from their own Revocable Delivery (RD1), which is a spend from the Commitment Transac- tion. The Breach Remedy Transaction will send all coins to the counterparty within the current balance of the channel.
(Emphasis by me.)
I do, however, not understand why this is a requirement. It seems to me that it's possible to design the Revocable Sequence Maturity Contract in such a way that only the signature of the Breach Remedy Transaction's issuer is required, not additionally the one of the redeeming party.
Is my notion correct? If not: Why not?