analog to digital to analog conversion

Potential stupid question alert.

There seems to be quite a movement of people favoring R-2R ladder DACs over chip based technology. A common impression is that the R-2R approach sounds less digital and more natural. When music is recorded, the analog to digital conversion is done using chip based converters, not some type of resistor ladder ... correct? So it would seem to me that a chip based solution that reverses exactly the digital encoding should be able to do a better job of restoring the audio back to its original analog state, retaining the least amount possible of "digitalness." What am I misunderstanding?