No, you are right. With the grip on the tiller in the "Fast" position the carburetor throttle valve (Butterfly valve) would be wide open (Horizontal). The adjustments are made with the vertical throttle shaft which changes the magneto position.

The carburetor throttle valve is controlled by the magneto cam right up to the point that the magneto hits the stop. Then it is held against the stop by the spring in the connecting link while the rod takes over from the cam to fully open the carburetor throttle valve. . . 😉