Correlation does not imply causation, and all that.
Anyone who has studied statistics in any context will know that correlation does not imply causation.
In this sense, it is always correct to say "Correlation does not imply causation."
In this case, correlation between studying and test scores would almost certainly imply causation.
But I will also say that you are very correct in pointing out the basic statistical mistake of implying causation from correlation.
However, most of these studies focus on various correlations, and correlation does not imply causation.
You are right, correlation does not imply causation.
Good comment about the risks of implying causation from a correlation.
It is important to clarify here that correlation does not imply causation, and rather identifies dependence of one variable on another.
The model must express more than correlation because correlation does not imply causation.