"Knots are produced when a limb is broken and needs to be sealed off by the tree."

Nononono. Study the structure of a tree (or any vascular plant). The stem, and the branches, are made of concentric tubes, an inner tube that goes woody in trees and my wife's broccoli, and an outer juicier bit- this gets gnawed by deer, squirrels and so on, leading to the tree dying, because it's the bit that carries the sugars made by photosynthesis down to the roots, giving them the energy to pipe water and salts up to the green bits up top. A knot happens whenever the system branches, because both the inner woody bit has to get through the side.