The entire point of USAMO problems is that they demand novel insight and rigorous, original proofs. They are intentionally designed not to be variations of things you can just look up. You have to reason your way through, step by logical step.
Getting 25% (~11 points) is exceptionally difficult. That often means fully solving one problem and maybe getting solid partial credit on another. The median score is often in the single digits.
That's true, but of course, not what I claimed.
The claim is that, given the ability to memorize an every mathematical result that has ever been published (in print or online), it is not so difficult to get 25% correct on an exam by pattern matching.
Note that this is skill is, by definition, completely out of the reach of any human being, but that possessing it does not imply creativity or the ability to "think".