The vertebral foramen
What is it, and what passes through it?
A number of structures pass through the foramen. These are the root of each spinal nerve, dorsal root ganglion, the spinal artery of the segmental artery, communicating veins between the internal and external plexuses, recurrent meningeal (sinu-vertebral) nerves, and transforaminal ligaments.
The nerves in the hand
Starting in the trunk of the body, the nerves of the arm and hand arise from the cervical and thoracic regions of the spinal cord as spinal nerves. These nerves merge to form a network called the brachial plexus before continuing into the arm. Five major nerves extend from the brachial plexus into the arm: the axillary, musculocutaneous, median, radial, and ulnar nerves. Each of these nerves carries information in the form of nerve impulses to and from a particular region of the arm and hand. Some of these impulses are sent from various parts of the brain and spinal cord; some come from sense organs located in the joints, ligaments, and tendons; and some come from nervous tissue in the muscles themselves.
In this paragraph it is specifically stated that impulses received in the hand by receptors, can come from the brain and spinal cord "and some come from nervous tissue in the muscles themselves."
The vertebral foramen is a part of the spinal cord, and forms a vertebral canal, the nerves running through it, and the impulses which are sent could be received by the receptors in the hand. Which could affect flexibility in both neck and extremities.