The Importance of the Digital Cable

Yes, electrical noise will be very important contributor affecting not only transmission (creating time jitter), but also polluting everything else. Reflection created jitter in cable plays separate role. Reflections will produce time jitter of the signal hence added noise on analog out.  Two cables that have exactly same shielding may sound quite different because of impedance mismatch (one is a better match to DAC's input impedance).

Yes, cable delivers digital information to D/A converter to produce analog (audio) signal. When this information is delivered in exactly same intervals then everything is always the same - perfect reproduction, but the problem is, that exact moment of D/A conversion can be affected by many factors and intervals become uneven (jittery). When this happens extra information is added to original signal. To understand this let’s imagine that you transfer constant 1kHz sinewave, but because of 60Hz noise moment of conversion (D/A clock) moves slightly back and forth in time 60 times a second. Now instead of pure 1kHz sinewave you will hear additional signals (sidebands) at 940Hz and 1060Hz at very small level. There will be many more, spaced by 60Hz, but because of smaller amplitude only first two (940Hz, 1060Hz) count. Amplitude of these sidebands will be proportional to amount of shifting in time (jitter).
These sidebands are extremely small, but still audible because they are not harmonically related to root (in this case 1kHz) signal. With many frequencies (music) there will be a lot of sidebands - practically added noise. This noise is proportional to signal level and without signal you cannot even hear it, but it is responsible for loss of transparency, loss of imaging, harshness etc.

So, now we know what happens, but why it happens? What can affect D/A conversion clock. To start with, this clock itself doesn’t have perfectly square edges and any noise in the system may add to edge (make it jagged) changing slightly moment of threshold crossing. What else? D/A clock has to be synchronized somehow with incoming S/Pdif signal, otherwise samples might get lost. It is done by taking average of S/Pdif signal word rate and using it to clock D/A converter. In spite of using average (no filter is perfect) timing variation in S/Pdif affect D/A clock. Where they come from? Electrical noise is obvious culprit. It adds to edges (making it jugged) changing moment of level recognition (threshold). Shielding, grounding, isolating etc. might help. It might be even worse for Toslink that being not sensitive to noise pickup is affected by system noise at both ends (Toslink transitions are slower).
Another culprit is reflection in the cable that adds to the edge (makes it jagged). This reflection happens when cable’s characteristic impedance is not matched to DAC input or Transport output. Beginning of the transition starts reflection from impedance boundary (usually cable’s end), that comes back and adds to rest of transition modifying its shape.

Characteristic impedance is very difficult to measure, so it is trial and error and expensive coax is not necessarily best match to impedances in your system. Shielding, of course is very important.

Hope it helps.

This is not true. As mentioned by several here; the "digital" signal is actually electric and any ic might do a ok job, just try. Don`t let the salesman fool you

This is not true.  As mentioned many times here digital signal is affected by time jitter (doesn't come in even intervals) producing added noise after D/A conversion.  One of the causes of the jitter are reflections of the signal inside of the cable on characteristic impedance boundaries.   Expensive digital cable might be (other than better shielding) not better than the cheap one.  It is all system dependent and better cable will be the one that has characteristic impedance matching better (especially to DACs input impedance).  Analog cables are likely to cause jitter since they are not designed for any specific characteristic impedance (not important for analog signals in audio band).  Some DACs might have strong jitter suppression but other DACs will be affected.  Jitter is the main cause why digital often sounds bright and harsh in comparison to analog.