Very few people achieved perfect scores on the SAT before the 1995 "recentering" (e.g., in 1987, only nine students got perfect scores). Therefore, if Schumer got a perfect score, he may be among the smartest men alive in the USA.
This was all before anything like an "SAT test prep" business existed. The makers of the SAT would not have yet been prepared for a concerted attempt by an aggressive group to "game" the test in this way. Thus, when Schumer took the test (probably multiple times), he may well have been the most "prepared for the test" of any student alive in the 1960s. He'd had years of defacto "SAT-prep" (seeing the actual questions used by the SAT), before the field of SAT-prep even existed. That this boosted the scores of a smart boy into the near-1600-range is plausible.
The way Kaplan, Schumer, and co. aggressively "gamed" the SAT in the 1960s is distressing, yet even "honest" test prep strikes me as at least a bit ethically dubious. If standardized tests are supposed to be about how smart (or how informed on a given subject) a person is, then highly-aggressively "prepping" muddies the waters, and can be seen as a form of non-punishable cheating. It tests what you studied, not what you know, if that makes sense.
See the Ethics subsection of the "Teaching to the Test" Wiki article:
Because of its shortcomings, the practice of teaching to the test is often considered unethical. A 1989 study on teaching to the test evaluated the ethical "continuum" of the practice, and identified seven practice points, ranging from most to least ethical:
1. General instruction on local objectives
2. Instruction on general test-taking skills
3. Instruction on objectives generally measured by standardized tests
4. Instruction on objectives specific to the test used
5. Instruction on objectives specific to the test used and using the same format
6. Instruction using a released test or a "clone" test that replicates the format and content of the test used
7. Instruction using the test to be used, either before or during test administration
The study concluded that the ethical boundary fell between points three and five, with points one and two being ethical and points six and seven being unethical.
In extreme cases (Korea) too much time devoted to test-prep seriously dulls the intellectual passions of teenagers.
A lot of what I've taught over the years in Korea has been test-prep, I must confess. It's been principally for TOEFL. Parents of Korean teenagers want this, for some reason. Korean parents really seem unaware/unconcerned when it comes to this "dulling the intellectual energy" effect of endless, mindless test-prep.
The lion's share of regular-schooling for Korean students is also directed towards test-prep, especially for their version of the SAT called the Su-Neung. Are the Koreans, after literally countless thousands of hours of test-prep for the Su-Neung test, really better-off -- "better-educated", better-informed-about-the-world, able to make more informed choices, possessing of more intellectual passion and curiosity -- than they would have been if they'd done no prep at all, and used that time for other purposes? Not from my (limited) observation. / The test-prep obsession is a manifestation of something else, which is harder to pin down, but test-prep is a "tentacle" of it. This "tentacle" seriously stunts the personal development of many Koreans, and (as I understand) many East-Asians, generally.
Fighting the System
A year ago, my coworker-friend C.H. (an American in his 30s from California) quit his job here in Korea, partly due to frustration with the above-described system. He spoke a lot about how bad he felt it was. In his final weeks, C.H. eagerly recommended this TED talk to all students. / You know how, in a certain kind of movie, when the good-guy is surrounded, outnumbered, and begins to run away, he tends to shoot wildly into the distance while making his escape, right? He's shooting at the bad-guys. The good-guy is hoping to score some hits, sure, but the shooting may be mostly for his own satisfaction, I think:"I fought the good fight and I did the best I could". C.H. was the good-guy, and each of his recommendations of that particular TED Talk was a bullet fired at the enemy.