> Charter schools throw a wrench into this as they typically don't support special needs kids, but still get district funding. This causes other schools in the district to look "worse" because their test scores aren't as balanced as before.

This is probably state-dependent, in California charters have the same obligations (with two different organizational ways of addressing them, either as if they were their own district or as part of the local district) as other public schools with regard to special education.