A circumstantial clause has two dimensions. Internally it is a complete sentence with its own constituents; externally the entire sentence functions as the state accompanying the earlier event.
Focusing only on its internal completeness may make it seem like a separate report. Ignoring that completeness, however, obscures why an explicit link can become useful. The rhetorical problem is to preserve its function as a circumstance rather than let it drift into an unrelated new assertion.