Yeah, it may indeed require some new Slack processes and discipline. But, the alternative would be account linking (like GH). Your interactions would have responses from Claude that are only visible to you if others didn't have the required permissions. It would use your credentials, etc.
That would defeat the stated purpose of collaboration/shared context, it would essentially just be another surface for your private Claude sessions.
Just gotta either decide not to use it or use it and not be willy nilly about the Slack channels in which it's provisioned.
