I read a lot (!) of reviews before going with AoPS, and the general consensus seemed to be that the kids that really liked it tended to be the highly visual-spatial, "start with the big picture and then derive the details" kinds of learners. It may not work so well for those that prefer to build up the details piece by piece to make a larger concept. One Mom perfectly captured the spirit of the comments I kept seeing, noting she tried AoPS with he twin boys, and her "whole to parts" learner loved it, while her "parts to whole" learner found it frustrating and unhelpful.
I have never read or heard anything like this, and this is not my understasnding of AoPS at all. I don't think they'd describe themselves anything like this either.
What is true is they try to get the student to learn something by solving a problem about it, rather than simply being told how to solve that type of problem first. That won't work for all students. But the student's "discoveries" are still somewhat incremental. They are not ever expected to have an epiphany where they suddenly see the whole big picture in a single vision.
