Acquiring an education at university level (at a reputable university) requires one to be able to grasp a coherent set of ideas and techniques that together form the tissue of established science.
A student's grasp of the subject matter is (in reputable universities) not tested by measuring if people can regurgitate the material (achievable by rote learning), but if they can *apply* the tools to a new problem and if they can correctly assess and explain the impact and importance of e.g. changing one or two basic propositions of the theory.
That is how you test if a student has actually understood something they learned. And no, the questions that result from this line of approach can't be found in the books and can't easily be prepared for.
Correctly answering questions like that demands knowledge (a student must *know* (i.e. have memorised) enough of the subject matter) as well as intelligence (defined as sufficient grasp of the theory and an ability to use the theory to reason with it (i.e. apply it), and (this is how you recognise very good students) the ability to reason *about* the theory).
So by and large, someone who is educated in a reputable field at a reputable university and has better than minimum passing grades is intelligent. If they can grasp, apply, and reason about one theory, they will be able to do the same with other theories. Those tend to be the people that go into research by embarking on a PhD (at reputable universities).
So there's the causal link underlying the correlation between intelligence and education.
Of course there are a fair number of diploma mills that focus on testing memory. There you don't receive an education, you memorise a syllabus and learn how to avoid saying anything not covered by the text you learned.