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It has very little to do with true knowledge of mathematics
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Who said "talent" had anything to do with knowledge of mathematics?
I have the same question as the OP; on the most recent AIME i received a 6 (and made the dumbest adding mistake on #11-i forgot to add a number to my final answer -_-). However, I think that everyone answering "I've never taken this test and I got in" doesn't really address the OP's question--does a 6 or 7 actually HELP you? USAMO, granted, seems to help alot--almost every USAMO qualifier gets into MIT. However, there doesn't seem to be a trend among those that can score in the 6s or 7s on the AIME. Almost as many get rejected as are accepted, or so I see with the trends on CC.
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Some may argue that you can practice for it, but I think it is like math class.
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?It's a fact that this test is study-able. Granted, it's a level higher than math class--those that even have a chance of doing well are those that, as you put it, consistently get 100s in class. However, it's DEFINITELY study-able (is that even a word?) The "people who could come up with the solutions on their own before they were taught it" don't really apply here...there are VERY FEW PEOPLE who are born knowing how to solve AIME problems without having done anything remotely like it!! Unless I'm wrong and have below-average-AIME-level-intelligence, but I studied for this test more than I've ever studied for a single class or standarized test. I remember the first time I took this test I got about a 50 for the AMC12s then .....I did AoPS book 1 which took me about two months, and then i did a month of practice AMCs (i screwed up the AMCs, and so kinda gave up and didn't study for the AIME) and I got a 114/6. I don't know what you mean by not being able to practice for this contest, but I definitely improved after doing ~3 months of practice.