Not to mention the fact that it makes a lot of sense. Statistics is not the only evidence supporting this theory.
I understand what you meant, it's an intuitive conclusion, one that doesn't seem like magic. But, something making sense usually does not correlate with or serve as evidence of it being true.
It's true that statistics is required to be sure if something is true, but it's a priori far more likely that a rise in violent crime is caused by a substance known to damage people's brains than by, say, the gravitational influence of Pluto. And we rightly demand careful confirmation when someone finds a particle traveling at a velocity greater than c than when it is found to be traveling at a velocity less than c.
EDIT: And more to the point, I hope you don't find the hypothesis that violence in the 70s caused leaded gasoline in the 50s as that leaded gasoline in the 50s caused violence in the 70s, and that you would agree that one of those two hypothesis needs more evidence before we accept it. Granted, it could easily be some more complicated net of causality, but just between those two.
But, there is a stark contrast between leveraging prior information to strengthen your estimates and stating that prior information serves as evidence or correlates with outcomes, which was my original assertion.
Either way, I'm a big fan of leveraging common sense (viz Bayesian approaches) so I can't disagree.