The assumption that accreditation and education must be done by the same organization is absurd, really. Public schools evidently have the exact same incentives. The answer is that third parties should be evaluating education, not administration making up numbers and giving themselves a pat on the back for doing so well.
Of course, teaching to the test isn't ideal. But it looks like the alternative isn't a well-rounded education, but not teaching at all.
Unless you think parents value "100% on their tests" more than receiving a quality education.
I trust a parent's judgment more than administrators looking to prop up their numbers.