When digital information is underexposed, chips will strain to record information in the deeper values, and in doing so will produce digital noise.
Ummmm. The darkest areas in the image will be just that - dark. Noise is only produced when you increase the gain (i.e. amplify the signal), so brightening/lightening shadow areas will increase their noise level - very simple. If they are important (more so than highlights) then underexposing them will lead to increased noise when adjusting later. Its got nothing to do with ETTR and lots to do with exposing for your preconceived requirement of output. ETTR in itself is in essence overexposing and as I have said before, can lead to tonal anomalies. So correct exposure must be made on the basis of the subject. Until we get sensors able to record much wider contrast ratios we are always going to be compromising somewhere. I don't see any real advantage to ETTR even in the low contrast conditions (which we compensate for by using flash) underwater. Gurus are great but actual practice is even better IMO.