Positive Training a.k.a. Positive Reinforcement Training a.k.a. No-Force Training (sorry, it goes by a lot of names) does not mean you permit your dog to do whatever she feels like.

The word positive in positive training comes from the idea that you give your dog something positive as encouragement to keep doing the thing you want her to do.

It doesn’t mean you’re always a super positive person who never sees the negative in a situation (although that can be a useful attitude from which to approach life).

For example, if your dog steals a piece of chicken off the table, you don’t just look at her and laugh and say “Go for it! It’s all good dude!” (unless it is of course “all good” and you meant that chicken for her, in which case...your dog is well trained?).

Instead, the positive training response in that scenario would be to take the chicken away if you can. You should also probably put her in a time out in her crate. Additionally, the absolute ideal response is to avoid that scenario in the first place. Now that your dog knows she can get delicious chicken off the table it will be hard for her to unlearn that. Reduce the opportunities for your pup to repeat behavior you don't want.

There are other positive reinforcement ways to deal with that too, but the point is, you should still correct your dog when she behaves inappropriately. It’s how you choose to correct that makes it positive training.