Third-degree burns are not that dangerous when limited in size. (I've had several others from motorcycle accidents, reckless play with fireworks as a kid, etc.)
I suppose WebMD was trying to put it in terms that are accessible to the layman, but "at the base of the spine" is colloquial and misleading. Sensory nerves are projections from neurons that have their somata (including their nuclei) in the dorsal root ganglion (DRG). The DRG lies OUTSIDE the spinal cord, within the dorsal (back) aspect of the vertebrae. "Base" has no anatomical meaning with regard to the spinal cord or spine.
The point is that if the nerve cell that innervates the skin dies, that means that the DRG cell dies. One cannot kill the "surface skin nerves" without killing the DRG neurons-- they are one and the same. The only caveat to acknowledge is that herpes can occasionally travel from the DRG into the sensory tracts inside the spinal cord proper. But this appears to be rare.