That is the INTENT, sure. But does it work? If you have someone that graduated from a school A and someone that failed to graduate from school B that is in an entirely different area, can you draw any meaningful conclusions? Particularly knowing that school A has no particular requirements on why you graduate, while school B does?
I'm far more likely to complain about "But when we disaggregate student performance scores by racial categories (white, black, Hispanic, and Asian), the rankings change dramatically." I wouldn't want to go too far with that before ensuring that I wasn't trying to curb swimming deaths by keeping Nick Cage out of movies: http://tylervigen.com/view_correlation?id=359
Removing graduation rates is definitely troublesome. Any school system could then improve its numbers by encouraging the worst students to drop out. Problem students both take more resources to educate and produce worse scores. That's bad for efficiency, but it is not obviously bad for society.
I am also troubled that they are using measures of performance in grades 4 and 8, but not something like SAT scores. I understand that SAT scores could be hard to get. But a lot of what people care about in an education system is how well prepared you are for college, and not how far along you were in grade 8.
The first statement is true. The piece would be a bit stronger if the researchers noted that by publishing in Reason, they're at the very least giving the appearance of potential confirmation bias. Your second statement makes an unsupported assumption though.
RE: SAT scores - not all students take the SAT, some students take it multiple times, the SAT is taken at different points in time per student, and it's a test that is so influential in college admissions that success on it is strongly correlated with wealth, as scores are best improved by tutoring on test taking strategy, not increasing general knowledge. I agree that grade 4 and 8 are probably not optimal to get a complete picture of education quality, but there is no reward to the student for doing well, so they're less likely to have spent substantial time investing in beating the test.