If we have a ball in a frictionless tube, and we begin to spin the tube about one end, the ball will exit the tube, correct? Indeed, there must be some centripetal acceleration, but then what force is causing the centripetal acceleration? The tube's normal force only acts in a perpendicular direction, so what force could possibly be causing the ball to rotate?
The ball will fall out of the tube, but I think this is precisely because there is no friction to supply the centripetal acceleration. There is still a normal force however this is not towards the point of rotation. Friction would supply a force along the direction of the tube. Since you cannot supply an adequate centripetal acceleration, the ball should fall out.
Remember, you must provide a centripetal acceleration to keep it in circular motion. If you don't have that, then no circular motion! This is simply Newton's first law: the ball would "prefer" to move in a non-circular path and must be coerced not to.