Simple. What one experiences in the typical road position is a torque about one's sit bones, created by one's upper body. This torque is resisted by counter-torques provided by the feet and hands. A torque is force X distance from the center about which it acts. So increasing the distance between your butt and hands and keeping the torque the same reduces the force necessary to create said torque. It's all true. A more stretched position reduces weight on the hands. And not only weight, but it also reduces shock forces on one's hands because the forearms are more nearly at right angles to the direction of said shock forces. Plus then the shock forces don't travel up the arms to the shoulders so much. It's more comfortable, but it does take some getting used to.

In the same manner, moving the saddle back increases the distance between butt and pedals and thus increases the counter-torque provided by the pedals.