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Even though you can learn contest math, it seems nearly impossible to do at that level without a great deal of problem-solving ability
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However, it's highly probable that there are people who have such problem-solving ability who just haven't qualified for the USAMO. You may be underestimating the number of people with such exceptional ability.
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Also, I find it hard to believe that a person getting a "B" would get better recs than the guy getting A+s unless there was some extreme difference in the level of difficulty of the high schools involved. So if person A has worse grades AND worse recs than person B, it is very unlikely that you choose person B over A. It's very unlikely that someone could do something that would offset this, because in reality there are very few people who actually are at the level to do something really outstanding outside of class in research...Even most Intel Finalist people generally just do some research project that their mentor suggested. Also, it's probably even rarer that someone finds a new subatomic particle but can't get an "A" in basic physics or calculus. Besides, it is extremely difficult to be creative if you haven't even mastered the basic rules of a scientific or mathematical field.
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Busywork. While busywork is a part of every profession, busywork in school is pointless busywork towards a figure with fiat value. Moreover, time in school is limited and valuable, and can be much better invested in a high school research project or competition. Sometimes, the grade for a class is overwhelmingly determined by a single exam (and then the person may just have been sick that day). Also, some students make mistakes and study exactly the wrong things and proceed to bomb the exam. As long as the mistakes are not consistent, they're fine. There are USAMO qualifiers who make the occasional B in an advanced math course (Caltech 2006 admissions thread).
Nonetheless, most of the rejectees and admits do have near-straight A's for their high school careers. It's just that some of the rejectees have more APs, extracurricular math/science activities, and post-calculus math classes than the admits. And the fact is, APs, extracurricular math/science activities, and post-calculus math classes are highly dependent on the school of the person and the nitpickiness of the student's counsolers (some refuse to let people place out of a higher level class), more so than the student's intrinsic aptitude.
I don't think that MIT is making all of the right decisions, but there are people with near perfect SAT scores, lots of APs, Calculus BC in 10th grade, and AIME qualification who nonetheless still struggle with theoretical mathematics courses (I know some). All of the abovementioned exams have absolutely nothing to do with the difficulty of college courses.
It may help to remind everyone that a B is context dependent. As I (jocularly) said in another thread:
I think we should all start a mass campaign to convince every Intel Semifinalist, every USAMO qualifier, every person with "insane stats", to get a B. That will make a B look less severe.