Does the Click End the Behavior?

It seems straightforward: we click to mark a desired behavior, and then we reinforce. The act of reinforcing the behavior necessitates a change in action: the horse eats the treat, the dog plays with its favorite toy, and the animal in the process of being reinforced no longer performs the behavior for which it was clicked. The click, therefore, ends the behavior. The phrase has become a widely-repeated tenet of clicker training. Yet, is it true?