Yes, correct. Dogs are smart! They know the difference between good leash manners when walking around the neighborhood, and what is expected from them during training.
Almost all of Gryff's OB was done off leash - he has a very high pack drive and ball drive, so he was just so happy to work. In protection he pulls like a maniac - the trainer we had from a few weeks ago took over line-handling for me when we were working a new helper, and the ex-military, national level helper got dragged down the field by my loose-leash walking dog.