Is it the group moderation or the forum moderation's problem if there's a pesky member causing problems?
No one is "responsible" for an overall topic. Every member is responsible for their own post(s) and the consequences of them. If a topic is made in a group and cross-posted to the mains, then people who reply are responsible for their replies. Anyone who sees the topic is capable of hiding/muting content or users. Since the Code of Conduct applies in and out of private groups, if someone makes a post that violates it and other members choose to hide/mute it, then that poster is accountable for their own actions. Or am I misunderstanding your question?