The more important point, however, is that a correlation between A and B does not imply that A causes B or B causes A. It could also be that unknown factor C causes A and B.
Your point is a very good one, though. If we view causation through a causal graph, such that vertices are variables and direct causal links are arrows (directed edges), a statement "correlation doesn't imply causation" can be taken to mean several things:
* From correlation, we cannot determine the direction of the arrow.
* From correlation, we cannot claim there *is* a (direct) arrow between two vertices.
* From correlation, we cannot claim there is even a path from one vertex to the other.