I disagree with the USAMO statement. It would be fine if everyone treated the AMCs/AIME just like the SAT - but it's not treated in such a way and consequently, those who qualify for USAMO are often those who qualify not due to inherent aptitude or motivation, but rather due to superior resources/more studying even before diminishing marginal returns with each additional hour of study/etc. That's true for the SAT, but even more so for the AMCs/AIME.
The collegeboard, incidentally, puts A LOT of research on the SATs. A HUGE HUGE amount (I've seen the charts, they are incredibly incredibly detailed). Words can't express the amount of effort the Collegeboard puts into collecting data about its tests, and in making sure that its tests would produce fairly consistent results in the same student from year to year (unlike the AIME, where score jumps in both directions are very common). This is certainly not something that the organizers of the AMC/AIME can put into the test. Such research is often needed to prevent the same people from having year-year score jumps on the SAT.
^lol, I sound so immature there. But yeah, the research the CollegeBoard collects is certainly amazing. I'm still naive, so my "threshold of OMG" is still low - that is, I would say OMG at a stimuli that an older person would find non-surprising. The collegeboard could most certainly produce an advanced math test of its own. :P
The best test would be one in which the applicant was evaluated at his maximum level of performance. Two conditions (a) all applicants invest substantial amounts of time and thought into doing the very best they can on the tests, and (b) the test is reliable enough such that an applicant at maximum performance would score in a consistent and narrow range. These conditions aren't exactly true for the SAT, but they work well enough for the SAT to be used in college admissions in the wide group of the population. The problem is that such a test doesn't exist for students who can already score near-perfect.
Also, another thread for the lurkers:
Caltech vs MIT for engineering
(in which Ben Golub and sakky pretty much exchange many of the similar issues, just 2 years ago).