I must agree with you. In the integration guide, the scheduled task is mentionned in Concept -> Incoming tasks.
However, if you edit that scheduled task in Site Manager, the task name is:
Integration.ProcessExternalTasks and is calling
CMS.Synchronization.IntegrationExternalTasksProcessor. In Reflector tool, the core inside
IntegrationExternalTasksProcessor class seems to call
IntegrationHelper.ProcessExternalTasksAsync() method. So I assume it processes the outgoing tasks only.
In the API documentation reference for IntegrationHelper class, the method
ProcessInternalTasksAsync exists as well, so I don't see why you couldn't write your own scheduled task that does the incoming/outgoing synchronization. You can find documentation about how to write custom scheduled tasks
here.
Unfortunately, my knowledge of the integration bus module ends here (not much in fact...). So i'd rather not go too far explaining.
Sorry.