It's probably true that 99.9% of music listeners don't know, don't care, and can't tell the difference. But a few of us care a lot, and it's sometimes very important. I've been recently obsessed with barbershop quartet music, where the tuning of chords is absolutely pivotal. The alignment of overtones from justly tuned chords is, if you ask me, the entire point of the genre. The "ringing" produced from the aligned overtones is, I would guess, noticeable to a large portion of people with rudimentary music education.
You make a good counterpoint, for barbershop. It's definitely a form designed to bring out the effect of these microintervalic adjustments. Of course, those cords are sung in just intonation, not well temperament :)
I probably could have phrased my comment a little bit more delicately, but my point was in reaction to the article, not the overall concept of tunings and temperaments. What drives me nuts are these "you're doing it all wrong" types articles about something that really makes very little difference to most people. Especially this one, in which the author really didn't bother to provide any auditory demonstration of a purely auditory phenomenon.
I get what you're saying. I'm a classically trained pianist (and this may be the problem) who has recently taken up the cello. When I'm tuning my instrument, a note on an open string appears to my tuner to easily fluctuate by 4-6 cents. (That is +/- ~2-3 cents.) The article mentions that the tunings often vary by just about this amount. (Some were larger, but many were not.) My ear certainly doesn't hear the fluctuation in pitch that much, and I'm trained (spent 2 years in music school at the university level, had honors theory). When I'm fingering a note, it can vary by even more, even when I don't think I'm moving my finger at all. It seems to me that typical listeners would have a hard time discerning those differences, though I suppose the differences are amplified when played with other notes.
https://en.m.wikipedia.org/wiki/Barbershop_music#Ringing_cho...
Two examples of fairly audible ringing (probably start a little before my timestamps to get a little context):
http://youtu.be/KpBRetTqnqQ at 3:07
http://youtu.be/z9L4QEptVRo at 4:23