I and my daughter have both done CLEP’s for specific reasons (for me, I am already pretty educated due to age, for daughter, she has serious academic challenges and will never finish without some shortcuts). Overall I think it is a shame for a student to avoid taking gen ed classes that way, unless the gen eds offered are truly awful. But that’s me. It sounds like your daughter may have some academic interests (unless the double major idea was for another instrument) and might enjoy some of the gen eds.
For some it can save money so if that is an issue, then it is a good idea!
On the terminology: many colleges seem to have “conservatories” (Oberlin, Lawrence, Bard, Ithaca) as do some universities (SUNY Purchase is one example) These would meet your definition of “schools of music” since they are on campus with other academic programs and degrees. 
I think the term “freestanding” clarifies this issue!