in the pictures, you can see that the rather agricultural tiller arms have a pinch bolt at the back. This is actually how they should be (and ordinarily are) made: bore a hole, split the hole on one side, pinch together with a bolt. The resulting friction connection should be what is transmitting the torque, any keyway or cross bolt should be just as a safety and also to get the tiller arm properly aligned during assembly. We know that the Alpha builders thought that a set screw provided this function. Those tiller arms had only one bolt, and not much depth to the section.
If one rudder blade was over and not coming back, most likely the tiller arm had simply slipped around the shaft, so that the blade could no longer be centered. The way most internal armatures are made, thinnish bar stock is welded to the tangent points on the post, forming a triangle behind the post, and the shape is foamed and covered (or sometimes covered with shells and foamed in place). These welds might shear (and probably did on the other rudder), but it is very unlikely that one side of the welds would shear allowing the post to rotate without obvious distortion in the blade (also any sea action would complete the process very quickly). It is equally unlikely that the triangle formed by the bars would distort enough to allow the rudder to turn 30+ degrees on the post, again without exploding the shell or other obvious damage.
On the other hand given the description and photographs of the steering gear, it is quite likely that the tiller arm simply slipped on the shaft, then stuck (perhaps galled) into the new position. This might have been easily remedied by loosening the pinch bolt and re-centering the tiller arm. If that was impossible one might remove the stops, or saw the tiller arm off (which would not have been underwater work). We do not know if that was tried (if so, no one mentioned it), we only know they were somewhat anxious to get off with a convenient connection home.