The quote is not calling a major chords a tetrachord; it's comparing major chords to the set of tetrachords (whatever the quoted person has in mind; the linked paper isn't immediately accessible to me), despite not being a member.
For the harmonic convention of chords based on stacked fourths, I've always heard it called "quartal" harmony, but my knowledge doesn't go very deep there.
In any case, wikipedia disagrees.
> In music theory, a tetrachord (Greek: τετράχορδoν; Latin: tetrachordum) is a series of four notes separated by three intervals
They meant (like Wikipedia says) that traditionally a tetrachord spans a perfect fourth (i.e., that's the interval between the first and last notes), not that it's a stack of perfect fourths.
As to the original point, any discussion about dissonance of chords is meaningless without mention of temperament: in the modern tuning system (equal temperament[1]) both major and minor triads are pretty dissonant, look at the thirds at the table in the section named "Comparison with just intonation" in that Wikipedia page.
We have been dealing with the tension between keeping thirds and fifths pleasant for centuries: very roughly, people used meantone temperaments[2] in the Renaissance (which had perfectly tuned thirds), then came the era of well temperament[3], and eventually we settled for the simpler equal temperament we use today with its nasty thirds (it has several other advantages, but "having pleasant major and minor triads" is not one of them).
[1] https://en.wikipedia.org/wiki/Equal_temperament
It's explained in the article, but I want to emphasize that "well temperament" was not a single thing, but various separate attempts at compromise. Bach wrote https://en.wikipedia.org/wiki/The_Well-Tempered_Clavier seemingly to celebrate the idea of tunings that sound acceptable in every key (without the wolf fifths of meantone temperaments), but it's not at all clear what specific tuning he had in mind, if any:
> During much of the 20th century it was presumed, possibly mistakenly, that Bach intended equal temperament, which after Bach's death became popular as the standard keyboard tuning, and had been described by theorists and musicians for at least a century before Bach's birth. Accounts of Bach's own tuning practice are few and inexact. …Despite the presumption of equal temperament, research has continued into various unequal systems contemporary with Bach's career; there is debate whether Bach might have meant a range of similar temperaments, perhaps altered slightly in practice from piece to piece, or possibly some single, specific, "well-tempered" solution for all purposes…
Personally, while I know on some academic level that our 12edo minor and major thirds are off by something like 14 cents, they don't sound unpleasant to me. I think it takes a specific sort of ear training to become really, er, attuned to purely consonant intervals and to notice dissonance on that level (which only produces real clashes in the higher harmonics).