Localization of a target flash is inaccurate when presented around the onset of a saccadic eye movement, and errors vary systematically with the target-saccade onset delay. We have recently shown that under head-fixed conditions these perisaccadic errors do not follow the quantitative predictions of current visuomotor updating models that explain these mislocalizations in terms of spatial updating. These models all assume sluggish eye-movement feedback, and predict that errors vary systematically with the amplitude and kinematics of the intervening saccade. Instead, we reported that errors depend only weakly on saccade amplitude. An alternative explanation is that around the saccade the perceived target location undergoes a uniform transient shift in the saccade direction, but that the oculomotor feedback is, on average, accurate. This 'visual shift' hypothesis predicts that errors will also remain insensitive to kinematic variability of much larger head-free gaze shifts. Here we test this prediction by presenting a brief visual probe near the onset of gaze saccades between 40 and 70 deg amplitude. According to models with inaccurate gaze-motor feedback, expected perisaccadic errors should be as large as 30 deg, and depend heavily on gaze-shift kinematics. In contrast, we found that the peak errors were similar to those of much smaller saccadic eye movements, i.e. about 10 deg, and that neither gaze-shift amplitude, nor kinematics plays a systematic role. Our data further corroborate the visual origin of perisaccadic mislocalization, and strengthen the idea that efferent feedback in the gaze control system is fast and accurate.