If you freeze frame, it would cause the digital source to output the exact same data per each frame per second. So if there is distortion caused by cable not up to specification, radom noise would be introduced in the form of digital artifacts. They would be so obvious as they would not look like as if there is a digital filter applied to the picture to make it look faded or details missing. Plus, since the data is constant, any artifact would not appear still, as the data stream is constant, any noise would be randomly injected.
Also, HDMI data is checksumed, see HDMI specification:
www.hdmi.org/pdf/HDMISpecInformationalVersion.pdf