I don't believe that quote is correct. The verse you are trying to disprove actually says "He who spares the rod hates his son."
This is by no means a blanket endorsement for beating one's children black and blue. That is a misconception! It is simply part of a larger idea called "DISCIPLINING YOUR CHILDREN". As any child psychology expert will tell you, a child who grows up without any discipline at all is heading for disaster.
It is possible to give your children PHYSICAL DISCIPLINE, as in NEGATIVE REINFORCEMENT (spanking, etc.) without BEATING THEM HALF TO DEATH.
To suggest otherwise is completely ignorant!
Your research (85% of inmates...) seems lopsided. Surely something more than how their parents disciplined them (or not) led them to make their bad decisions? Are human beings really that one sided? You failed to mention if the inmates were raised in "loving, Christian" homes, or were the offspring of crack whores. Wouldn't that make a difference? How about individual choices, regardless of how they were raised? Your information is skewed. Bad science.
"Is there a loving, tactful way one can beat their children?" No. A beating is a beating. Not all corporeal punishments qualify as beatings. Learn the difference, or remain ignorant!
Is there a loving, tactful way one can DISCIPLINE their children?
Personal experience. I have been spanked, and I have been beaten, so I know the difference!