1,5 and 7 is still a triad in my book and it's also a chord, but one in this case that isn't Major or minor.
You can have dissonant chords if you like - practically any random collection of notes will be a chord that can be named. We've not even touched on inversions - which once you start swapping the notes around often suddenly become a totally different chord. We usually say chords have to have 3 different notes, but a guitar power chord might only have root, fifth and octave - and sometimes just the root and fifth - and it still makes that chord type sound.
What confused me was when he said he used to play triads and not tetrads - as if this is a way of playing, when chords are really just what works for a song - and you use as many notes as you want. A simple close triad with root at the bottom works higher up and sounds horrible lower down - and the more notes you play in the lower register the easier it is to get a really muddy sound. With five fingers on your right hand you can have 5 note chords if you have the dexterity and spread.
It only bad in my book when you follow, for example, a song where the lyrics are on the page with the chord symbols, and it says EM7, and you play an E Major triad missing the 7th, or it says C6, and you play C. However, if you play Em as a simple triad, and somebody else provides the C - that works for me, musically.