The shoulder and the spine are intimately related. The arm sits in the shoulder blade, which sits next to the spine. All are connected by a complex system of muscles, ligaments and joints and influencing one will influence the other.
Take for example the spine, if you bend forwards, the shoulder roll inwards. Extend backwards and the opposite happens.
Strengthening the muscles around the spine will not only help the back, but also help the strength around the shoulder blades and the arm. Stretching the spine and keeping it mobile will help the flexibility in the shoulder and arm.
If the spine is stiff, you will need to use the shoulder for a greater range of movement placing more stress through it. Maintaining strength in the spine will take more load from the shoulder and help protect it.