^Good question, Soundslikefog, and it is indeed one of the things that could have been made more clear in the article.
I don't know the exact way things work, since I'm not so informed on the technical side of these things, so take this with a grain of salt, but the way I understand it is like this:
The last thing that happens before your analog signal gets turned into the signal on your computer, is that it gets converted by the A/D convertor. Depending on your samplerate, that convertor creates a filterslope that removes all the information above that limit.
So even if you have all kinds of saturation with infinite harmonics and ultrasonic information going through the analog chain, as soon as it hits the convertor, it gets rolled off to remove everything that we can't hear/use. The point where the Nyquist theorem comes in, with all the fold-back issues, is right after this stage, so the problem described in it will only happen to the filtered signal that is being transformed in digital information now.
To have no foldback into the audible range, we require a samplerate of 2x the maximum frequency we want to hear. Since humans are limited around 20kHz, if not less, two times that gives us a samplerate of about 40k. Hence why that 44.1k mark is so popular. You could of course go higher if you have the diskspace and processingpower for it, but in an ideal case, there should be no audible difference.
However, not every converter is designed equal or with the best of the best parts, so it could be that a convertor has a slope that isn't ideal for the 44.1k setting. It rolls off too much or too little, and thus the results are coloured in an unintended way. In that case it could very well be that you up the samplerate, and suddenly the recording sounds like it is supposed to sound. At that moment, it is natural to think: hey things sound better at a higher samplerate! But as mentioned in that article, the reason that it sounds better is because the 44.1k samplerate filter hasn't been designed the way it should have. If a higher samplerate sounds better on your convertor...well, absolutely use it! But keep in mind WHY it sounds better.
With plugins it's different, because plugins are already working with the band-limited sampled recording. Let's say it's recorded at 44.1k samples. The plugin then introduces new harmonics that would go beyond the bandwidth in that recording. And everything that goes above that will then be mirrored back, resulting in unexpected results. So that's why those plugins have the option to extend that bandwidth, do their thing, and then bring it back to the old samplerate. The foldback will then again be in the inaudible range, and be removed from the signal when it goes back to 44.1k samples.
Again, all of this is from what I have understood from what I have read about this subject so far, so I may be off the mark! Maybe someone else can correct me on this