The answer is that there wasn't really any inconsistency between Atkinson's speech and Bush's, even though one man wants to abolish tests and the other wants to institute them, because the underlying idea is the same: to use tests as a tool to encourage students to master a set body of material in school.
This is not the underlying idea of the SAT in fact, the original idea of the SAT was almost exactly the opposite: to use a test as a tool for discovering and whisking away to universities a small number of students of extraordinary ability, not to try to find out how well most students were learning or most schools were teaching.
The SAT began its life as an intelligence test, which its makers believed measured innate mental ability. Carl Brigham, the test's inventor, was part of the team that developed the Army intelligence tests during World War I; the first SAT was an adapted version of that test. Henry Chauncey, the founding president of the Educational Testing Service, and his boss during his previous job as an assistant dean at Harvard in the 1930s and '40s, James Bryant Conant, chose the SAT as an admissions test because Conant saw it as an IQ test. In those days, high school was a relatively new institution in the U.S. There were actually more high schools then than there are now, but they were decentralized and of highly variable quality. Conant wanted to accomplish two goals: primarily to make sure the best minds got to top universities so the nation could make use of them and secondarily to make the student bodies of Harvard and schools like it more academic and more national. The SAT was attractive to him because it seemed then to factor out the quality of the taker's education.
Atkinson was addressing a situation that Conant and Chauncey didn't imagine. The SAT, now with millions of takers a year, has become a national fetish. A large portion of the high school student and parent population believes it is the main determinant of admission to a selective college, which in turn is the main determinant of one's eventual socioeconomic status (both propositions that the test's makers heatedly deny). High school students and their parents also believe that scores on the all important test can be raised by spending hundreds, even thousands, of dollars on courses that teach you tricks for outwitting the test (its makers deny that too). Real estate values in suburban communities vary with the local high school's average sat scores, even though the test was not designed to measure schools.
Although few people are aware of the SAT's direct roots in intelligence testing, lots of kids have a vague sense that the test measures how smart you are, and they internalize the score as a lifelong measure of their innate worth. The SAT is like a medicine that accomplished its original purpose identifying a few hundred especially gifted high school students every year but has had unusually powerful and harmful side effects.
The University of California, like most state universities, used the SAT to make itself more selective and to set itself apart from the public high school system of its state. In the early 1960s, the university accredited California high schools and admitted many more students than it had room for, a large portion of whom dropped out or took longer than four years to graduate. With the advent of the SAT, the university stopped monitoring high school education and started accepting fewer students. Over the years, applications soared, and a series of increasingly bitter fights began over who would get the increasingly precious slots, especially at the university's flagship schools, Berkeley and UCLA. During the late '80s and early '90s, Berkeley admitted half of its freshman class purely by a numerical formula in which SAT scores were the most important element. Because of the substantial gap among the races on the SAT, the schools could maintain a substantial minority presence only by explicitly setting test scores aside which led to a revolt, culminating in a successful state ballot initiative against affirmative action. Surely Atkinson proposed abolishing the sat in the hope of diminishing some of the nearly unbearable pressures that the adoption of it had generated.