I think you've got it backwards. Since correlation is bidirectional then the reversal should NOT be meaningless.
Sorry, bad wording on my part. I don't mean the reversed phrase should be meaningless, but that it should not mean something different than the unreversed phrase. However, it clearly does mean something different, therefore the implied relationship between smart and drunk is not bidirectional.
That being said, I missed the possibility of a 3rd underlying factor. The title is agnostic about this possibility.
"Drunks are smart people"
The reversal should be meaningless if the title only implies correlation, since correlation is bidirectional. However, since the reversal is not meaningless, then the title must imply causation.