I think it's all in the geometry. Let's first assume that knees don't rotate, and our legs are stiff straight. Consider the rotation of your leg about your hip and focus on the trajectory of the kicking foot, some sort of circular arc. Think of it as a pendulum.
If you kick standing vertically above the ball, you will hit the ball with your foot at the very bottom of the pendulum's cycle, the lowest point. It's like dropping the pendulum onto a ball that is placed right beneath the axis of rotation. On impact, the pendulum's velocity is horizontal.
If you lean back, your hip will move horizontally away from the ball, or the pendulum's axis is moved away from the ball. When dropped, the pendulum will not hit the ball at the lowest point but at a "later" point in the movement, and the impact velocity will have a vertical component.
Add this : if you think of the ball not as a point mass (which is in fact compulsory since your hip moving away means you will hit the ball in a different place on its surface since your leg hasn't stretched), then the pendulum hits the under side of the ball towards the sky when ball is not right below, whereas it will hit it higher and slightly towards the ground if the ball is placed under it.
I think that accounting for knee rotation doesn't make much difference.
Why does leaning forward guarantee not only a lower shot but also a better controlled one ? I have a vague idea about this, as a casual football player, nothing to do with physics or biomechanics. I would say that when you lean back, you let physics do the work, swinging your leg about your hip, whereas when leaning forward it feels to me like there is less swinging and more voluntary muscular action.