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thomblake comments on Causal Diagrams and Causal Models - Less Wrong
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"imply" in the traditional phrase is used in the strong sense. You can have a correlation between 2 factors without there necessarily being a causal relationship between them.
If you can exclude coincidence, which is a question of confidence and what kind of data the correlation is based on, then you can say that the correlation does necessarily involve a causal relationship.
Well that's just what I think. If you can show me how that's wrong, then please do. Except I don't think you can.
That's begging the question, if by "coincidence" you just mean those cases where there is a correlation which does not involve a causal relationship.