I just remembered an old 'statistic' I once read about.

It seem that at one time, there was for several years and almost perfect correlation between the sales of alcohol and the salaries of college professors.

I believe it was used in a statistics course to demonstrate the dangers of drawing too many inferences.....

I don't think that was a fair 'demonstration'. It was just the professors trying to claim that it wasn't them doing all the drinking!
It doesn't disprove the inference.