Bob, the quality of the disk is obviously an issue with LP, because here the mechanism for recovering the sound is mechanical, the quality of the "road" is all important for getting clean sound. But in the digital world, bits are really bits as they say, no matter how dusty, rusty and bedraggled they are the information about the sound is still identical: at that point "perfect" sound can still be recovered.
Why it often isn't though, is because the bits of electronics well away from the CD reading device are too flakey; the idio... , sorry, designers of the audio components actually believe what makers of various electronic parts say, that you only have to do such and such to get optimum performance.
So a simple scenario is this: an only reasonable CD player plays a roughly made CD. The actual physical bits of the CD player that do this then have to work hard, lots of sharp current pulses ripple through the player, the dodgey power supplies go all sloppy and inject muck back through the transformer which infects the house circuit which feeds the other components, and also corrupts the electronics which feed the signal across to the amp side of things. Also, digital circuitry has to work hard to correct all the errors; this is computer stuff, which generates very nasty radio frequency interference, spraying in all directions.
So, a so so player with a so so CD throws a lot of electronic dirt and muck around the place. The answer then is to either to make the player's job as easy as possible, by putting on a super "good" CD; or, work hard on the CD player to stop it being a bad neighbour to the rest of the system; or, isolate the badly behaving CD playing process from the good electronics, by putting an electronic black box or shield around the audio, analogue side of things ...
All of these techniques will work!
Frank