"If you play purely by ear, then of course all this is purely academic but if you play music in a situation where the norm is to play from written music then it is definitely of practical importance."

since most music is in equal temperament it is not of practical importance, it is of importance in some forms of classical harmony writing, as regards correct protocol,
it is important in other temperaments other than equal, but it bears no relationship to whether someone is a good teacher.
But since the guitar is an equal tempered instrument, the guitar teacher would have been correct in f he had said that on the guitar b sharp and c occupy the same fret, as do g# and a flat, so what you call them whilst you are playing is not important, because they are in effect the same bloody note, this is probably what he meant.