I think it's the other way around, Doc. Hal Galper talks about how in jazz everything goes by too fast for conscious thought, which is why "you don't need to be smart to play jazz".
Firstly, I sort of disagree with the quote specifically. When I jam freeform, I don't do what's in my head at the moment, I do what's in my head few seconds or measures ago. I think ahead so that I'm not behind when it's time to do stuff. I get my ideas for what to do next based on what everyone else has done, is doing, and likely will do.
But ideally, you want your mind to be as clear as possible and surrender to your natural instincts, letting all the internalised listening, playing and watching make things happen. I think this applies to arranged music too - internalise it and let it pour out in performance.
Interesting. As noted above, I certainly can't say that my head is clear when I play, especially when I jam. I'm constantly organizing all the changing shapes and textures of the music into patterns, and sometimes I even try to keep track of several options, or I'll hold onto the feel of a fill that I liked how it fit into the music, waiting for the other guys to set up that same situation again. I kind of set those things aside while I listen for the triggers and leads.
In fact, when I'm playing in front of people, and my mind goes blank, I tend to panic. It means I'm out of ideas or I've gotten bored and I'm not paying full attention anymore.
IMO it's no accident that so many great musicians were crazy hedonist ratbags. Met a number of musos whose heads doesn't interfere with their instincts - great for playing, not always social or practical life.
You may have noticed that my personality is often somewhat forward and frequently abrasive. My friends often joke that I seem to be missing any sense of filter, and will just convey whatever pops into my head.
That's the theory. I never learned how to consistently get my head out of the way. How I play very much depends on how centred I am.
Heads are funny things. Mine really likes to decide that it's going to shut down and refuse to operate when I'm faced with either the "record button of doom" or the "scrutiny-of-my-drum-teacher of doom". Yet, I can be more than comfortable playing live in front of whomever. Go figure.