What if the connection is what enables the child to settle, self-regulate, and thereby correct his or her own behavior? Parents don't have to administer correction to a child who is calm and in control. It seems to be (and maybe I'm late to the party) that "connection before correction" is a spin on "feel better to do better."
I like my new interpretation much better. For me, it just sits more comfortably in the PD realm. Correction, when it was coming from a parent, always had a faintly punitive ring and made the connecting part seem like a set-up. Now when I think about it, I see a parent lovingly helping a child to calm down and the child then no longer "needing" to "misbehave."