I suppose in a very general sense what you say is correct. A lot of people say digital is digital, it is either received or not received. But if you look at the details there are still some slight differences but which I don't fully understand. Have a look at this article: http://www.audioholics.com/education/cable...ble-bench-tests - in particular read about the test equipment and the eye pattern.

Another theory of mine, yes bits are either 0 or 1. But a signal isn't just 1 bit, it's not a case of cannot receive a 0 or 1 signal = complete failure. In one second megabits of signal is passed through the cable, what if the cable is not capable of transmitting all the bits perfectly? What if only 99.9998% are ok and the 0.0002% is not received? How does this affect the audio/video?

Should ask that salesman if he dares to do blind test.

or maybe, it should be: I did not hear any strange discomforting abrupt sounds that is associated with digital audio data loss during transmission via digital cables....

so what happens to the audio and videowhen error correction in digital signal fails?

Ok let me see if i can convince you.

Do you know how binary (0, 1) system works?

A LCD tv is made of millions of pixels (or dots). 1920x1080(2 million pixels) for a FullHD tv
Each pixel is encoded by binaries. If you see your GC properties, there is an option to choose 32-bit color or 16-bit color, this is what represents a pixel.
32 bit means 32 (0 or 1) to represent the color that a pixel can display.

So take an example that you are displaying a fat straight line with some blur around the edges (which means grey pixels around it)
These grey pixels can never becomes black pixels which will make the line looked clearer. WHY?? Because the cable can never know what encoding to make it display a black pixel. It doesn't have a chip/DSP for such algorithm.

Similarly, if the picture is a well defined straight line with no grey pixels around it, a capalang cable can never make the pixels grey in color. At most (if the build quality is lousy), the encoding for that particular pixel got lost during the transmission and the TV will just display a weird color for pixel (white i think).

Similarly is for audio. Do you know how analog signal is encoded into digital form?