No, I don't think they have that wrong. I think that Peterson doesn't specialize in child psychology, and isn't aware of the literature about spanking's ineffectiveness.
The only caveat is this: how are they defining good and bad results? I think they are measuring things like anxiety, with the view that anxiety is bad because it's unpleasant. Obviously, a child who's spanked regularly will have more anxiety than a kid who is let free to do whatever he wants. But will that latter actually be more effective in adult life, especially in tough times?
So that's the only thing I'd say if I were to argue: how do you define whether something "works"?
The only caveat is this: how are they defining good and bad results? I think they are measuring things like anxiety, with the view that anxiety is bad because it's unpleasant. Obviously, a child who's spanked regularly will have more anxiety than a kid who is let free to do whatever he wants. But will that latter actually be more effective in adult life, especially in tough times?
So that's the only thing I'd say if I were to argue: how do you define whether something "works"?