The specific notes (call them scale degrees if it helps) are derived from the root major scale by stacking thirds. Having arrived at those three notes, any rearrangement by changing the sequence will seem to be shifting their intervals. And, laid out on a linear scale or around a note circle, it does. Your interval descriptors in the quoted text are correct. But the three scale degrees, when derived from the C major scale, spell a C major triad. Nothing else.
If those exact same three notes were being analysed from the framework of a different major scale (a different key signature if you will), that would be a wholly different story.
For example, those notes can all be found in the key of G.
G, A, B, C, D, E, F#.
In the key of G that would be an E minor b6 (no 5th).
That is a bit of a rabbit hole leading to nowhere really.
So come back up and think only of one key signature at a time from which you analyse its triads which are all built on stacked thirds.