Nope, your logic is flawed...this is how I arrived at my idiot-savant theory...
One of the arguments in the past was that left-handedness was caused by brain damage, since discounted I think. But, gawd can you imagine how smart I was before I suffered the damage. Wow!
Just kidding, but not of necessity about the logic. It applies to many aspects of socio-cultural reality.
“But those who have been under the shadow, who have gone down at last to elemental things, will have a wider charity” - Herbert George Wells -