Dana --

I find no one by that name enrolled in a Kentucky unit in service of either side.

Being a Kentucky resident, there's no reason to expect this man to have enlisted. Most Kentucky men elected to stay out of the fighting. As you noted, Crawford was a physician, so unless another doctor was available in the community, citizens at home would have need of his services. For that matter, if he decided to enlist, who would take care of his wife and family?