"If I offered my dog a treat for herding the cattle, she would look at me like I was crazy."
This is because positive reinforcement training is not about treats. It's about REINFORCEMENT. If giving your dog treats is not increasing behavior, treats are not a reinforcer.
ALL DOG TRAINING IS ABOUT REINFORCEMENT
If you want your dog to do things, you need to use reinforcement. Positive or negative, behavior comes from reinforcement. Think about how your training paradigm uses reinforcement, and you will instantly understand how to put it into practice better. Success builds on success. Even if you are using corrections, they are meaningless unless the dog can succeed at the task following the correction. The important part about the choke chain is not when it is tight, it is when it is LOOSE.
"Some dogs just need corrections."
What bothers me about this is not so much that dogs are being corrected, it's the implication that if you bolt away from the dog so that he flips over and is dragged five feet, the dog will now instantly respect you and all your training will go swimmingly from that point on for ever and ever until you ride off over the rainbow together on matching unicorns. I am not against dogs getting physical corrections, provided the correction is administered within a system that the dog understands. I am against training that doesn't do anything, that only addresses the behavior in the moment and not the behavior in the future.
Corrections are not ABOUT punishment. They ARE punishment, in the psychologist's use of the term ("don't do that"), but what makes a correction more than just punishment it that puts the dog back in correct action; the sit correction is a sharp jerk upwards because it will cause the dog to sit and thus be correct (this chain is an example of P+ -> R-, since the collar is tight when the dog is not sitting (P+) and loosens when the dog is sitting (R-)). A correction is punishment with information about how to receive reinforcement. It's the difference between a teacher marking the wrong answer in red, and marking the right answer in red.