In high school, my music teacher would always tell me when tuning the bass after the fifth fret on the string above, to tune the G string after the FOURTH fret on the D string. I never really understood this, as the fourth fret would be a G flat, but I never questioned her. But surely a music teacher with a university education wouldn't just be wrong about something like that? Is there a reason she would tell me to move my finger to the fourth fret on the D string?
That's for guitar, not bass, and it's because for whatever reason, guitar tuning is imperfect. On a guitar:
e (1st string) B (2nd) G (3rd) D (4th) A (5th) E (6th)
…you tune the B (2nd) string to the 4th fret of the G (3rd string) string above it. But on a 4-string bass, the 1st string is G:
G (1st) D (2nd) A (3rd) E (4th)
…and, as on guitar, you tune the G to the 5th fret of the D above it.
So the imperfect tuning thing isn't something bassists normally have to worry about. Unless you're playing on a bass with 6 or more strings, as such basses include strings both below the G and above the E.