Ozpeter, prof_peabody and I have exchanged a few private messages over the past day or so. He is very courteous and sincere in wanting to help me grasp what seems so obvious to him.
From his message posted above, it's clear that he thinks of the sampled waveform as if the analog signal's value was defined only at the discrete moments in time for which a sample has been stored. From that premise, his conclusion is indeed quite obvious (more samples = greater accuracy), and quite a few people share it, including some prominent audio professionals. The premise is mistaken since the signal is still defined at all points even though it is being represented in the short term by discrete-time samples. But let's take the belief seriously and see what predictive value it offers.
THD+N is a straightforward indication of the difference between input and output, stated as a percentage of the input signal's amplitude. When the output of an audio recorder fails to deliver whatever was presented to its input, that difference can be characterized as either noise or distortion; THD+N measurements aren't even concerned with which one is which; any difference for any reason is counted equally.
If prof_peabody's belief is correct, the THD+N of (say) a 1 kHz sinusoid recorded at (let's say) -10 dBFS on a 96 kHz, 24-bit digital recorder should be less than half the THD+N of the same signal as recorded on a 44.1 kHz, 24-bit digital recorder. Yet the THD+N of a digital recorder actually turns out to be a function of its bit depth, not its sampling rate. If you believe as he does, this outcome must be baffling. A 96 kHz recording is a "more accurate" rendering of the original analog waveform, so why does the analog output of the system not resemble its input any more closely than in a comparable 44.1 kHz recording? Why is this supposed "greater accuracy" not measurable, nor audible, nor visible on an oscilloscope, nor discernable by any other objective means?
I think that many people are fooled by their visualizations of the digital samples, and by failing to understand what happens when the discrete-time signal is converted back to a continuous, analog signal. I'd like to point out that to prof_peabody's credit, he clearly recognizes how important that is--many people do not, unfortunately.
Once the sampling rate is already greater than twice the highest frequency of interest, a "more accurate" recording of an analog signal cannot be achieved simply by increasing the sampling rate--a statement which proceeds directly from Shannon's sampling theorem (60 years old this year). Shannon's work isn't intuitively obvious and it's not visually convincing, either, without some math. Its only virtue, really, is that it explains, correctly predicts, and allows people to design linear, discrete-time systems such as digital audio recorders.
--best regards