In martial arts thinking is not supposed to happen because a person who thinks is not fast enough in a fight. As a result (at least in Chinese martial arts) the training consists in conditioning the body so that it will automatically react in a certain way when the fight occurs.
In a similar way, I think people who play instinctively have an easier time dealing with Melee's hardcore speed and the extremely high amount of information they have to process. At least as far as the "technical" aspects of the game are concerned (knowing timings, spacing, priority, etc.).
I've always thought knowledge of the game data is somewhat trivial, and I've been surprised lately by the amount of information the other Italians are, unlike me, aware of. There's no need to know the frames in which Falco can be shield grabbed during pillaring, as long as you know that pillaring is not invincible. And there is no need to know at which % certain comboes can be landed as long as you have the natural skill to follow up an enemy and keep a combo going.
Lately, however, I've started to think that active thinking can be very helpful while playing. If on the other hand it means drawing some of your attention from the "instinctive" side of the game, on the other one I think it might be more effective in preventing stupid behaviour on your part as well as in finding out and exploiting your opponent's habits.
In a nutshell, the way I see it is: Instinct helps you understanding the game (spacing, timings, priorities, etc.), Logic helps you understand your opponent (habits, good/bad decisions, etc.).