I investigate the nature of the transient nebulous companions to the sungrazing comet C/1882 R1, known as the Great September Comet. The features were located several degrees to the southwest of the comet's head and reported independently by four observers, including J.F.J. Schmidt and E.E. Barnard, over a period of ten days nearly one month after perihelion, when the comet was 0.7 AU to 1 AU from the Sun. I conclude that none of the nebulous companions was ever sighted more than once and that, contrary to his belief, Schmidt observed unrelated objects on the four consecutive mornings. Each nebulous companion is proposed to have been triggered by a fragment at most a few tens of meters across, released from the comet's nucleus after perihelion and seen only because it happened to be caught in the brief terminal outburst, when its mass was suddenly shattered into a cloud of mostly microscopic debris due possibly to rotational bursting triggered by sublimation torques. The fragment's motion was affected by a strong outgassing-driven nongravitational acceleration with a significant out-of-plane component. Although fragmentation events were common, only a small fraction of nebulous companions was detected because of their transient nature. The observed brightness of the nebulous companions is proposed to have been due mainly to C2 emissions, with a contribution from scattering of sunlight by the microscopic dust. By their nature, the fragments responsible for the nebulous companions bear a strong resemblance to the dwarf Kreutz sungrazers detected with the coronagraphs aboard the SOHO space probe. Only their fragmentation histories are different and the latter display no terminal outburst, a consequence of extremely short lifetimes of the sublimating icy and refractory material in the Sun's corona.