I mean when one tries to cheat by broadcasting an outdated commitment transaction. As far as I've understood, the cheater needs both signatures to spend from the force-closed multi-sig address.

I'm typing this example to ensure that I get it.

1. Alice opens a 0.1 BTC channel with Bob.
2. Alice wants to send him 0.02 BTC, so she signs a transaction with two outputs: A) to_local (that can be spent by her after x blocks) and B) to_remote that can be spent by Bob instantly.
3. Alice sends him the commitment_signed message, which contains her signature.
4. Bob responds with revoke_and_ack, where he's inserted his new commitment point (for the next revocation public key) and the secret for the previous commitment so that Alice can punish him in case he cheats. (Which wouldn't make sense in our case as he'd earn 0 sats)
5. Bob sends her the commitment_signed message, which contains his signature.
6. Alice responds with revoke_and_ack where she's inserted her new commitment point and her secret for the previous commitment.

Is it correct? I confess that the terminology is hard to grasp.