There is a well known problem of interface jitter from transmitting the clock signal along with the data. I would agree that in the scheme of things this form of distortion is usally pretty small nowadays (compared to other problems like speaker distortion) but nevertheless it provides an example of why a digital cable might make a difference.
The jitter issue you are referring to is completely independent of the cable and symptomatic of the chosen bit stream framing format (tying the video and audio signals together in a certain way). Changing cables from a cheaper brand to more expensive brand has no effect on the jitter issue you are referring to in your post. Given the same exact lengths of cable and gauge, a $20 cable and a $2000 cable have the same exact jitter issues...
Likewise, the jitter levels introduced are imperceptible. Except by people with overactive imaginations, but they are hearing their imagination, not jitter... :D