Both amplitude noise and time noise (jitter) can potentially matter. The DS is less sensitive to input jitter than most other DACs so this is less of a problem. But amplitude noise can become jitter and jitter can become amplitude noise any time a clock interacts with the signal (both illustrations are qualitative not quantitative):
Any ground loop (which is hard to avoid with non-optical connections) can transform the flux in the loop into a current around the loop (and vice versa: noise in a loop can radiate via the ground loop.)
Any noise that get’s superimposed on any analog signal in a system can become audible: low frequencies simply raise the noise floor, higher frequencies get modulated down into audio frequencies by any non-linearities in the following circuits (e.g. the parasitic diodes in the input transistors, etc.) (E.g. like a crystal radio.)
Just because an Ethernet connection uses a transformer on each end doesn’t mean that it doesn’t transmit noise: noise near DC is certainly attenuated a great deal but noise near the frequency of the nominal signal frequency passes right on thru the transformer (and hopefully is mostly dealt with by the common mode and differential mode chokes in the Ethernet receiver and transmitter connectors.)
USB’s noise is a little worse, there is ground noise that’s hard to get rid of, but there’s also noise on the VBUS line (which needs to be there for proper signaling when a device or hub is added or removed.) Also the data lines run parallel to the ground and VBUS lines so there’s more cross talk than one would like.
None of these issues normally cause any data errors, but when you want 120dB S/N in your audio, the results of any of these effects have to be less than 1 in a million relative to the audio everywhere.
There are ways of dealing with all of this and various systems will have different needs re. that noise - you’ll find some here who get better sound with Ethernet and others with USB.