I also rely on the "inner voice" for reading and writing. But I can skip that when programming. I think it's related to how you learn that language in the early stage.
When I am designing the solution, I still have the inner voice. But when I'm implementing in code, I can do it almost "brain-lessly", even fine when listening to music.
I'm not sure how do I do that, but I guess because I do it a lot, so I can do it as familiar as walking?
Edit:
Maybe because I didn't learn programming by listening to teacher, instead I learn from books and trials. I guess it's more like walking / playing sport, you don't need explicit inner voice to guide your body movement.
