Why does the ring finger not move independently?
The reason for this phenomenon is in both the muscular structure and neural connections of the little and the ring finger. Lets start with the following diagram:



As you see (click on the image to see full version), the fingers contain extensor muscles for movement. However, the index finger and the little finger have separate extensors, because of which they can move more independently as compared to the middle finger and ring finger, which contain a common extensor muscle called extensor digitorum. Some people lack the interconnections between these extensors, and can thus move their ring finger quite easily. One can also achieve this through practice.

Now, as to why the ring finger moves easily when moved along with another finger, have a look at another image:



The fingers are connected to brain via two nerves: 


radial nerve, which connects with thumb, index finger and one side of middle finger
ulnar nerve, which connects with little, ring and the other side of middle finger


As you see, the branching between these nerves is what causes dependence of the fingers on each other for movement. Since the nerves for ring finger and little finger are intertwined, it becomes difficult to move each of these fingers separately. Similarly, you may find it easier to move your ring finger along with your middle finger. But you can easily move your middle finger independently because it gets signals from radial as well as ulnar nerves.

Thus, it is the combined effect of muscular and neural anatomy of ring finger which causes this effect.

PS: Since the effect is due to the neural and muscular anatomy of the ring finger, I don't think surgery would help in this case.

References:


Wikipedia contributors. "Extrinsic extensor muscles of the hand." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 29 Jan. 2017. Web. 27 May. 2017.
Ross and Lamperti, 2006, p. 300
Flexor Tendon Anatomy - Medscape
Wikipedia contributors. "Median nerve." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 1 May. 2017. Web. 27 May. 2017