From my peers those that grew up in strict Muslim and Christian homes, where they did get corporal punishment, they were much better behaved. That has also translated into their success now they're in their 30s.
But those who also got corporal punishment in more dysfunctional households have had terrible outcomes. Their "punishment" was probably much closer to child abuse that those from the other group.
I was not spanked my self so I have no personal reference, only that I was far worse in self discipline than the first group. I'd have expected this study to show some correlation between self discipline and spanking. I can't help but think they've conflated child abuse and hitting out of anger with spanking.
That said, I'm no expert.