Let me add some fog! It is possible to make a golf stroke such that the golf shaft always points at the target line. Such an action requires the least amount of physical effort by the golfer since all of one's effort is eventually directed at the ball. However, because of the human's bio-mechanical structure, to do so, the club shaft will always be swinging on very different inclined-planes. Dunn was wrong and Hogan very wrong, but they both were effective golfers.
Yes it would be possible with on a putt. You would have to bend way over to do so.