Agreed, though repeated measurements weren't mentioned so I thought it was important to emphasize that finding a correlation in one measurement cannot be taken to imply causation, which sounded like what OP was saying.

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.

Indeed. I think it is also important to note that the unknown factor can be something very abstract. For example if you measure the oscillations of two pendulums with the same properties, they will also be correlated, but simply because they are driven by the same underlying physics...