In order to meet its cutting-edge scientific objectives, the Square Kilometre Array (SKA) telescope requires high-precision frequency references to be distributed to each of its antennas. The frequency references are distributed via fiber-optic links and must be actively stabilized to compensate for phase noise imposed on the signals by environmental perturbations on the links. SKA engineering requirements demand that any proposed frequency reference distribution system be proved in "astronomical verification" tests. We present results of the astronomical verification of a stabilized frequency reference transfer system proposed for SKA-mid. The dual-receiver architecture of the Australia Telescope Compact Array was exploited to subtract the phase noise of the sky signal from the data, allowing the phase noise of observations performed using a standard frequency reference, as well as the stabilized frequency reference transfer system transmitting over 77 km of fiber-optic cable, to be directly compared. Results are presented for the fractional frequency stability and phase drift of the stabilized frequency reference transfer system for celestial calibrator observations at 5 and 25 GHz. These observations plus additional laboratory results for the transferred signal stability over a 166 km metropolitan fiber-optic link are used to show that the stabilized transfer system under test exceeds all SKA phase-stability requirements within a broad range of observing conditions. Furthermore, we have shown that alternative reference dissemination systems that use multiple synthesizers to supply reference signals to sub-sections of an array may limit the imaging capability of the telescope.