Jerry,
It is not uncommon for tires to pick up stones and invariably they are flung somewhere in the rotation trajectory of the tire tread. If the stone can hit the spinning fan, it can be readily cast into the radiator. The fact that you had three of them would lead you to believe that there was some location in your route that had a significant quantity of the right size stone to fit your tread pattern. It is a travel fact of life that this occurs.
The most likely case is that whatever mud flaps and wheel well shield that you have in place allows a trajectory path to the fan blades. Some folks, especially those that travel in Alaska have indeed created a stone guard around the fan blade area. As far as a stone being cast towards the mud flap and then reversing direction and finding its way to the fan blade, it is possible, but I do not think this is as likely as some more direct path like inadequate mud flaps behind the tire exposing a more direct shot towards the fan blades. Try and view from behind your rear tire tread if there would be a direct path from a stone leaving your tread to a fan blade. Most fans including mine have some portion of the fan blade that rotates outside of the shroud.
Later Ed