[ThinkingPlus]

Excellent, we've got to the core of the issue very quickly.
When we speak of the rock's point of view, we are talking (I hope) about what you would see through a tiny camera attached to the rock. Through this camera we would see such interesting sights as a stationary rock (because we are attached to it), the centre of motion (the boy's hand) would be stationary, and everything else in the world would appear to be in the process of being flung from away from the centre of motion. The centrifugal force (away from the centre) will neatly balance the centripetal force (toward the centre), but no net force is acting on the rock. It is not being flung out. It just sits there stationary in the camera shot.

The problem is that this is not a helpful frame of reference because it is not an inertial frame of reference. We have to do all sorts of fudging if we are to explain why all of the objects (grass, trees, etc) are being flung away from the centre.

If we want to apply the usual laws of physics we need to look from an intertial frame of reference. The string pulls in on the rock (centripetal). The string pulls out on the man (centrifugal). The force on the rock is not balanced, and the centrifugal force only affects the string and the boy.

The frame of reference is always a choice. The laws of physics in this case are invariant regardless of frame of reference. However, the explanation of what is going on varies. A rotating reference frame is proper during the downswing since that is the frame of reference the golfer lives in so to speak. You wish to keep things in a non-rotating reference frame because it makes the centrifugal force explanation less applicable.

This whole argument is splitting hairs about reference frames and centrifugal force. It is pointless to the golfer. One will get the right answer whether one invokes the concept of centrifugal force or explains the phenomena as inertial resistance of the clubhead mass. Basically it all comes down to what folks will understand more easily. Centrifugal force explanations are more intuitive to understand for the majority than inertia which is why it is more generally taught that way in universities across the world (to physicists). It is nice that you learned your physics a different way, but the answers all turn out the same. I suspect we will just have to agree to diagree, Jack.