Phase distortion refers to the alteration of the phase relationships between frequencies in a signal, which can be perceptible. In this paper, we discuss a special case of phase distortion known as phase-intercept distortion, which is created by a frequency-independent phase shift. We hypothesize that, though this form of distortion changes a signal's waveform significantly, the distortion is imperceptible. Human-subject experiment results are reported which are consistent with this hypothesis. Furthermore, we discuss how the imperceptibility of phase-intercept distortion can be useful for machine learning, specifically for data augmentation. We conducted multiple experiments using phase-intercept distortion as a novel approach to data augmentation, and obtained improved results for audio machine learning tasks.