The private high school I went to costs $15,000 a year for day students now and the average SAT was over 1200, I really doubt that the DC schools are getting over 1200 SATs (I guess that is 1800 now with the new SAT) despite spending twice as much money per student. Hell, 28k is what the boarding students paid.
SAT scores do not have much to do with the quality of a school. It is more of a test of IQ. Private schools get higher SAT scores because smarter people with higher IQs go there.