You have the ability, from the manage bulletins page, to create 'linked copies' of a bulletin in other zones. When changes are made to any of these bulletins, the linked bulletins will receive the updates. By design, you can only create or edit linked bulletins if you are an admin or have the 'manage bulletins' permission in 'all zones'. A known limitation of creating linked alerts is that the mechanism for disabling alerts does not respect the same permission requirements as the creation of the linked bulletins.
This means that anyone with the permission to disable an alert in a zone with a linked alert will be able to disable all of the linked copies as well.