“BA students get grad students for studio teachers”
I think that this quote may not have been aimed at students doing a BA in music on an instrument or voice, rather I think the quote was where kids do music in college but do not major in it. Universities with music schools can have rules that non majors cannot use the faculty of the music school for lessons (depends on the school obviously), likewise for performance non majors may be in their own orchestra and chamber programs. In programs with that segregation, where the student goes let’s say for a degree in computer science but does music “on the side”, they very well may end up getting lessons from grad students. I could be wrong, but this was my read of that quote.