The term “positive” has at least two meanings in dog training. One is positive, as in dog-friendly. In that sense, Dog’s Best Friend Training is all about positive dog training. We train with food reinforcement or clicker training and do not use force, shouting, or other “negative” forms of coercion to train dogs.
The other use of “positive” in dog training is as a technical Learning Theory term. In that sense, there is “positive reinforcement” and “positive punishment,” among other things. In those terms, “positive” just means you’re giving the dog something, in the mathematical sense of addition. You’re giving treats or giving pain/annoyance. So in that usage, “positive dog trainer” doesn’t make sense.
Positive dog training is the way to go!