The point of a third fastener is not so much overall strength as it is to reduce flexing. When the gun or rifle is fired the action tends to spring apart and slam back together. This what causes the piece to eventually loosen or go off face. In order to do this the third fastener must be well fitted. If not, it accomplishes nothing. Today, many pieces will see so little use that there is no danger of going off face with ot without a third fastener. The doll's head with no bite can be effective because the center of rotation of the barrels on firing is not the hinge as it is when opening the action.

Incidentally, this is why proper lubrication is so critical. The lubricant acts as a cushion to spread out the impact.