Yes but  the truly great private schools are really just a few:  Iolani, Punahou, Mid Pac, Le Jardine a  few others.  There is one on the big Island.  Most private schools are Catholic schools which are probably not that much different from the public schools.  Some are special schools for special kids.  I think a measure of a good school is basically how many percentage wise go off to college and are successful there.  Iolani and Punahoe are basically at 100%.  I think the Catholic schools are probably better than the public schools but are far from 100%.  But I admit it has been a long time since I had contact with this information. 

As for an external audit, I am not against it.  Not sure what it would accomplish though.  A common characteristic of our private schools is that they are not cheap.  But they are when compared to elite private schools on the mainland. I think those can easily run 30 to 40,000 a year.