Three years ago, the report of a solitary radio burst was thought to be the first discovery of a rare, impulsive event of unknown extragalactic origin (Lorimer et al. 2007). The extragalactic interpretation was based on the swept-frequency nature of the event, which followed the dispersive delay expected from an extragalactic pulse. We report here on the detection of 16 pulses, the bulk of which exhibit a frequency sweep with a shape and magnitude resembling the Lorimer Burst. These new events were detected in a sidelobe of the Parkes Telescope and are of clearly terrestrial origin, with properties unlike any known sources of terrestrial broad-band radio emission. The new detections cast doubt on the extragalactic interpretation of the original burst, and call for further sophistication in radio-pulse survey techniques to identify the origin of the anomalous terrestrial signals and definitively distinguish future extragalactic pulse detections from local signals. The ambiguous origin of these seemingly dispersed, swept-frequency signals suggest that radio-pulse searches using multiple detectors will be the only experiments able to provide definitive information about the origin of new swept-frequency radio burst detections. ; Comment: 2 figures, 1 table, accepted to Astrophysical Journal Letters