Anecdotal observations:
From what I could tell, the success of the school was due to three things:
1. Parents who had available time, money, and energy to devote to the school. This would likely be less true in a lower income area, but as has been mentioned elsewhere, could account for higher average performance of schools that parents actively chose to put their kids in, regardless of location.
2. Excellent staffing, mostly due to the attractiveness of working in an environment with more freedom to innovate.
3. That the environment was different enough from the huge suburban public schools nearby that some students would perform better in that kind of environment.
One other thing I noticed that I haven't heard mentioned before, which is a situation that is unique to looking at the upper end of public schools and income brackets rather than the lower: the school I went to was not good at playing the college prep game. All the courses were difficult, so nobody had any "honors" courses on their transcript. GPAs were generally lower. Fewer extracurricular activities were available because of the size of the school. These facts resulted in a lower number of students going on to prestigious post-secondary institutions than you would expect from an otherwise high performing school.
ALL of these observations point to the conclusion that Charter schools are really just an "alternative", and naturally some alternatives will be an improvement and some will be a failure.
I like this article because it indicates that charter schools specifically help marginalized groups (black, poor), which fits nicely with the idea that having alternative environments in general is good for some students, and also matches my personal experience. (I promise this is the only time I will ever claim "white male nerd" as a marginalized group.)