I see a vast difference between "spanking" and a "swat", the former of which we didn't do to our children but the latter we did on occasions?
The study defines spanking as an open-handed slap to the buttocks or other extremities -- and your "swats" sound a whole lot like the study's "spanking" to me.
Ever try to have a rational discussion with a one-year old? Children have the remarkable ability to turn off the sound coming from parents' mouths, so talk, talk, and more talk sometimes amounts to no change in behavior.
Please understand: The study found that spanking is statistically linked to negative mental health issues and anti-social behaviors in people who've been spanked. The findings would remain the same even if you had every reason in the world to spank your children.