In all honesty and with all due respect for Altec, I couldn't disagree more.
When a CD player is used only as a transport, thus feeding an external DAC via its digital output, things like transport jitter and digital cable quality will have a significant say. If the external DAC re-clocks the digital signal, then every transport and digital cable will yield identical results, provided they are "bit accurate". In such a case the DAC "carries the burden" of sound quality alone.
If the CD player is used via its analog outputs, then better players will produce significantly better sound. The analog stage in the players, their internal clock accuracy, DAC(s) and power supplies quality and the interconnects used will all contribute significantly to the overall sound.
The sound of high quality CD players is smooth yet detailed, with a beautiful tonal balance and full bodied sound, with a tight bass foundation. The lesser ones sound harsh, thin and aggressive.
The better the overall system, the more prominent the differences.
I was one of those thinking of interconnects and speaker cable as "just wire" and, boy, was I wrong. It took only a listen to AudioQuest products and all that wrong belief changed in a hurry.
The only thing that didn't and never will change is my desire to respect everybody's opinion, no matter how different from mine.