I guess the argument should have been that once you cross a certain threshold, cable quality doesn’t matter. That was of course also true for analog signals (human senses are only so good), but the transition from good signal to bad signal might have different characteristics with digital signals.

While a image from a analog signal will only get noisier and noisier as signal quality decreases, images from a digital signal will first show artifacts and then just stop displaying altogether. That’s a rather sudden transition. One second the signal is there, the other it's gone. Something like that just doesn’t happen with analog signals. (I’m basing this on my experience with terrestrial digital broadcasting – could be totally wrong for HDMI connection but I doubt it.)

I would guess that how sudden that transition is has something to do with the error correction and the codec of the signal. How many wrong bits can the error correction reconstruct? And, as soon as the wrong bits get past the error correction, how many wrong bits can the decoder handle and still reconstruct a image (albeit one with artifacts)? It would certainly be interesting to know how that problem was solved for HDMI connections. If you know the maximum bit error rates for your cables figuring out which are the right ones should be easy, given enough testing :)