A large portion of the SAT is knowledge of English vocabulary which obviously has nothing to do with IQ.

The mathematics questions nearly all use the same basic rules and are presented in the same format, and can easily be learned and trained.

SAT prep courses are ubiquitous and expensive because they work. Do people without training do well? Sure. Do people with training still do poorly? Sure. But a good SAT question would be "does this mean that training doesn't help or that there isn't a correlation between training and success?" because the obvious answer is no.