this is discussed in https://claude.com/blog/agent-identity-access-model
From reading that and materials on it, it seems unclear if – let's say you do what's done in the demos on the site and 'dispatch work' from a thread in a shared channel (e.g. from some discussion) – that if any one of your coworkers replies below you and says, "Actually, could you fold in <blah> as well?" that Claude wouldn't listen to them and thus derail the work.
We do signal to Claude that there's a difference between a conversation's initiator versus incoming participants and we've found that in situations where people disagree on an approach, Claude patiently waits for a resolution while correcting any misunderstandings.
It's also worth mentioning that since Claude has its own identity, a coworker cannot enter a thread and commandeer _your_ identity; you collectively steer how Claude acts with its _own_ identity (it opens PRs as itself, browses Datadog as itself, etc).