But the reason why your digital TV shows the correct screen is because the cable transmitted the "digital" bits between your DVD player and the TV correctly. If you have a poorly made cable you will get bit errors. Electromagnetic interference from other A/V equipment could also cause bit errors. A well made cable with twisted pairs, proper shielding (few people do this correctly), and well formed connector crimps will prevent those bit errors. With bit errors, what your awesome Blu-Ray player decodes off of the Blue-Ray disc will not be what is shown on the screen (assuming there isn't bit error correction in the TV, etc.).

And your speakers are playing an analog signal. Cable quality matters even more there.