It could also indicate that the student is good at things that require one time short-term massive effort, but has difficulty maintaining a sustained effort.
It also may indicate that, while the student can memorize information and respond in a fairly topical manner, they may not have the ability to go very deep, as is required by essays, lab reports, or providing proofs in math.
While I think that high scores add a bit of extra information, it is much less than GPA.
In aggregate, though, SAT/ACT scores can say a lot about a school. A school with consistently high GPAs in rigorous classes, but low average test scores indicates grade inflation or some problem with teaching the class, while the opposite indicate either grade deflation, or issues with the administration of the tests.
While there is a good amount of variance around the slope, GPA is correlated with test scores. When this correlation is pretty weak, it means that something else may be going on.