I think Positive Training is complete crap - at least the evangelical kind. As pp points out, you must be clear and not go "No no no no no no" about everything, but only positive training can be as confusing to a dog as telling it off all the time.
Hardcore positive training relies on distraction - but that is no good if you are not there. They will still do the unwanted behaviour if there is no one leading them away from it. They need to know that certain things are wrong, or places out of bounds.
Dh actually got into a row with the trainer at Positive Training, when she was declaring that you must distract your dog from going in the oven when you open it. Dh was saying this was hopeless if a dog was in danger - you must be able to stop it doing something immediately, not faffing around encouraging it to look elsewhere.
We all know how children turn out whose parents "discuss" their spirited behaviour with them and "negotiate" over outrageous demands.
We tried Positive Training (we walked out) and Kennel Club Training (left by mutual agreement - ie thrown out
) until we found a lovely personal trainer who did the kind but firm route.