I suspect there's a high degree of self-selection bias involved in the success or failure of a charter school. That is, charter schools that do well do so because they are full of motivated students. It would be interesting to see any research that examines this aspect.

Personal anecdote: I grew up in a small town in ND where there are not a lot of socioeconomic disparities. Almost everybody was lower-middle class, with a few very poor. Everybody went to the same school and had the same teachers. It should not come as a shock that those who did well in school also had parents that were supportive and themselves educated. Those who did poorly were generally children of uneducated blue collar and farm workers. While poor teacher quality may have some effect on student achievement, I suspect factors outside of schools' control play a much larger role.