For the lack of a better way to say it, this is something I've been trying to figure out for myself. When you play BJJ, do you stay present and mindful of yourself and the situation, or do you just go all zen, blank out and just do whatever? I can see both sides of the argument having good points. It gets a bit confusing for me, though, as each side has some really credible support.
For example, Saulo Ribeiro is one of those who advocate the no-mind-let-your-body-know-what-it-knows-to-do style of rolling. He quotes Rickson(?) by saying "if you think, you are late. If you are late, you use strength. If you use strength, you get tired. If you get tired, you die." (source: Jiu-Jitsu University - IMHO a freaking incredible resource that was worth every cent!) That says it all so I won't try to elaborate.
On the other hand, Roger Gracie prefers to stay present and think his way through matches. To paraphrase him, "it's like chess. You've got to think. If you don't use your brain, you're going to lose" (source: Arte Suave vol. 1). It's really not as though you could argue with the man, based on his results. It is of course valid to note, though, not everyone is 6 foot 4, trains with a number of the greatest sport BJJ players alive, is super-strong, and has freakish Cobrinha-level technical ability - all at once.
For myself, I've noticed big results when I don't actively try to think my way through things. In rolling in the gym, or in competition matches, some of the best stuff I've ever done came in the absence of conscious thought. And on the other side, when I lose in competition, it's because I tried to use my head and work stuff out - while my opponent is already acting.
Which is not to discount engaging the mind and applying problem-solving skills to BJJ. I get a big kick anytime I'm able to have a game plan when I roll,and then implement what I can and adapt on the fly. For me, it feels really awesome if I can go in with an actual strategy. Just being able to read the situation and use tactics to get by is something I find amazing. It doesn't happen all the time, but when it does, it's really quite cool. This must be how rock climbers feel.