"It's all in the wrist" as they say.. yes, of course the hand connected to the ball was moving at this speed (or higher) at the time of throw.
This is the same in many other sports like volleyball or tennis. Untrained athletes keep one or more joints stiff during the movement which means they lose the maximum speed and also risk injury due to the added inertia of the arm that has to be accelerated by the shoulder muscles.
A good throw or volleyball spike works by folding the arm into a smaller shape in the beginning of the throw, which reduces the angular inertia allowing the shoulder to accelerate the upper arm. After a while, the upper arm muscles start to accelerate the lower arm + wrist combo, with the wrist a bit twisted, reducing that inertia. And finally the wrist is accelerated by the lower arm muscles. All these accelerations add up to a huge speed at the wrist-end.
Check out the hit at 0:29 in this beautiful slow-motion video