Only if the frequency being recorded is half the sample rate (a.k.a. the Nyquist frequency) or less. That's the case for that nice pure sine wave in the exampl

Only if the frequency being recorded is half the sample rate (a.k.a. the Nyquist frequency) or less. That's the case for that nice pure sine wave in the example, but in more complex cases you'd absolutely be losing information. Whether the lost information matters of course depends on the frequency range you can actually hear; in the case of CD-quality (44100Hz) audio you probably won't notice any issues unless you're a dog (or unless you're taking a higher-sample-rate recording and downsampling without any kind of anti-aliasing), but the article discusses a PCM chip that natively supports 32552Hz and is receiving a signal that was naïvely upsampled from 16276Hz. Especially in the latter case, you absolutely will hear the information loss.