The rule applies to the batter-runner becoming a runner regardless of how the player became a batter-runner. And when was the last time you saw a runner "walk" to 1B? In many cases, the player runs if for no other reason than be prepared to advance should there be a mishandling of the ball and/or make sure the BR is in the defense's mind.
That is what I meant, I can see rounding of 1B on a walk, but running through 1B on a walk doesn't make any sense to me.