While not common, it was not unusual for a body to be brought home for burial. In fact, it was during the Civil War that embalming began to become widespread for the purpose of bringing them home. Considering the transportation problems and widespread irregular activities around Batesville at this time it is actually more likely the body would have been returned home following the Civil War. The possibility also exists it is merely a marker and he is buried in Little Rock. One of my own ancestors has a marker in the family cemetary while he was supposedly buried about 15-20 miles away. This occured in 1864 and demonstrates the travel problems of the time as the family was unable to even retrieve his body from that distance following his murder. So, unfortunately all the scenarios you put forth are possible.

David