You're right that the GP is misusing the word 'harmonics', but the NYT article is probably not talking about combinations of tones produced by two flues when they say 'harmonic' either--they probably just mean that the scale itself sounds 'nice', which actually follows the more ancient sense of the word 'harmonics' which, for the ancient Greeks, was the study of tunings, temperaments, and scale designs. In other words, the scale sounds like modern music because it's a pentatonic scale.
Which brings me to what you were saying about music universals--there is, indeed, much cultural variation, but there are a number of commonalities--the pentatonic scale, is actually supposed to have been arrived at independently in many cultures, which isn't that surprising because it's what you get if you iterate the 'simplest' interval other than the octave, and the diatonic scales come from iterating that twice more.
There are also lots of universals about interval choice--melodically or harmonically, simple ratio intervals like 5ths are usually preferred, and you aren't going to find a culture that prefers minor 9th leaps to perfect 5th leaps, except Webern et al., of course.
There are also general cognitive constraints--for instance, most cultures have 5-7 note scales, which is supposedly tied to the size of working memory.
