The Nature of the Injury:

Carson's C7 vertebra in his neck was shattered on impact. The C7 vertebra is one of the lower and larger cervical vertebra. Carson was very fortunate to have broken only that vertebra. As one of the larger vertebra in the neck, it allows for more swelling of the spinal cord than the other vertebra.

Carson's spinal cord was not severed completely, it is severely damaged however. 

When there are injuries to the spinal cord, the spinal cord swells, which usually shuts down many of the nerves and functions of the body. The swelling can last for a number of weeks. Until the swelling goes down it is difficult to know what functions are gone permanently and what will come back. Carson is currently paralyzed from the nipple-line down but has use of his arms. 

Here is a link describing some of the typical outcomes of spinal cord injuries, broken down by vertebra. http://www.spinalinjury101.org/details/levels-of-injury.