They are wrong. Terminology is important.
Octaves are always perfect, as there is only one kind. 2nds, 3rds, 6ths and 7ths have two flavors: minor and major. 4ths and 5ths have three flavors: perfect, diminished, and augmented.
Western music is based on the major scale, everything is named in relation to the corresponding interval in the major scale, starting on the root.
I'd say Western music is based more on the 12 tone equal temperament system. Much of post WWI music is atonal or serial. And if we back up to Bach and before, Pythagorean just tuning was the system du jour. And before that church modal systems where perfect 4ths were considered dissonant.
Bach paved the way for 12 tone diatonicism with the Well-Tempered Clavier.
But I agree with learning your intervals based on a major scale