I am not referring to any specific CD/DVD player. In our hypothetical CD/DVD player, the entire song can be uploaded to RAM (i.e. computer memory). This is very inexpensive. Once the song is in RAM which is a digital circuit, it can be read out and processed by the other digital circuits of the CD/DVD player. These circuits perform error correction decoding and filtering. These are typical circuits in any CD/DVD player.
The key point here is that once the song has been uploaded to RAM, the transport is no longer part of the signal path. It is effectively non-existent. You can think of an Ipod Nano as a CD/DVD player which has the song loaded into RAM. Of course the loading of this data is performed from a PC and not a transport.
Once the digital signal has been processed by the digital circuits, this signal has to pass thru a D/A converter. The quality of the D/A converter as well as the clock which clocks the D/A converter can effect the sound quality. If the clock is sufficiently jittery, you will hear this.