(All that said, I do believe there is a genetic component in whatever it is we mean when we say “intelligence”–although we definitely mean many different, unrelated things to different people–in addition to the significant impact of parenting, home life, and of course education. The last item is of course the most easily controlled, so that’s the one I and most others focus on, and much of the research suggests that the single most impactful variable in education outcomes is teachers.
A great teacher can boost a kid 2 grade levels in a subject and a poor teacher can drop a kid a grade level or two, so that’s a tremendous factor.
I’d also argue that students who work hard often end up being pretty “intelligent” by whatever metric you use, because some of the few things we know about academic “intelligence” is that it’s related to acquisition and application of knowledge, that it’s not a permanent, set quality, and that it can be nurtured–or, of course, squandered.)
The SAT and ACT probably measure intelligence to some degree once the opportunities, background, and experiences of students are controlled. For example, if you compare native English speakers to non-natives, they will perform better on the SAT almost every time just because it rewards people who have spent years developing skills that match what the SAT requires. This doesn’t mean that the non-native speakers are less intelligent in any way.
SAT and ACT may not be totally irrelevant to whatever you think “intelligence” is, but the only thing a test can test is how good you are at taking that test.