George, Find A Grave Memorial # 87674412 for Richard B. Pittman has an In Memory Tombstone for him along with his photograph. The site indicates he was buried in a National Cemetery. In my opinion it all depends upon the research ability done by the person doing the biography at Find A Grave. Some are very good and some not so good. The National Cemetery Administration disagrees with the person doing the biography at Find A Grave. It would appear the In Memory Stone was done post 1963 and appears to have been done rather recently. And there does seems to be a connection between the Pittman and Thomas family. He was living in Marion County, Mississippi according to the 1860 census but his wife is also buried in Walthall County in the Thomas Cemetery.
While not all Confederate dead at Chickamauga were brought back home for burial some were. So the question now becomes which site is correct Find A Grave or the National Cemetery Administration? You would have to try and find out where the NCA got their source of information for him being buried in the Thomas Cemetery and I don't believe they would use a source from Find A Grave. And you would have to try and find out from the Find A Grave author why he or she believes he was buried in a National Cemetery. Only after analyzing the two sources could you make an intelligent decision. In my opinion the NCA would trump the Find A Grave author insofar as a creditable source at this juncture. The Confederacy would have had open to them at this time period the Western and Atlantic Railroad which went to Atlanta. Were there any railroads that went near Walthall County in late September or October 1863 and were some parts of the railroad destroyed or held by Union forces in Alabama or Mississippi in route to Walthall County?