I use the terms "negative emotions" and "positive emotions" with my students. I don't think Dr. Bracket is denying there are positive and negative emotions - it's the basis of the entire positive psychology movement.

My understand is that he is addressing people who judge the negative emotions as 'bad" and, without investigating them, and try as hard as they can to escape them.

To be mindful of them is to acknowledge them rather than just try to squelch them because they're "bad."

You can acknowledge that positive emotions/attitudes like joy, appreciation, gratitude, compassion, kindness, etc without setting up a battle with anger, fear, sadness, etc. (in fact, the less you fight anger, fear, etc, the more quickly you'll be surprised to discover they spontaneously transform into strength, courage, etc)