Since we're discussing semantics here, "deep thought" is not something I'd think as mindfulness meditation either: you're not supposed to be chasing your thought while meditating. You should just be observing them as they come ("the intentional, accepting and non-judgmental focus of one's attention on the emotions, thoughts and sensations occurring in the present moment." as you said), and then let it pass by, which is pretty much actually the opposite of deep thought.