Your information from the pension application and history of the 37th Mississippi Regt. is correct. Problem is, unlike other members of the 37th Mississippi Regt., MRB has no service file, no prisoner of war record, nothing to substantiate his claims made in the pension application. As mentioned earlier, records of the 37th Mississippi are complete through May 1864. For instance we know that RBB was kille don May 9, 1864 from company rolls. If MRB actually served with the 37th Mississippi Regt., we would expect him to mention the seige of Vicksburg, a major event in the history of that command. In any case, if he really was captured as claimed, we should have prisoner of war records for MRB during 1864-65.
After his release from prison in 1862, the only record I can locate on this man is filed under the name Mathew R. Barnes (Baines) with the 54th Alabama Regt. The soldier claims to have deserted on Dec. 10, 1864, entered Federal lines voluntarily and took the oath of allegiance at Nashville TN. Deserters were then released under condition that they remain north of the Ohio River during the war. It is not unusual for Confederate veterans applying for pension benefits to claim to have been captured, when records show they actually went over to the enemy as deserters.
As a post-war resident of Clarke County, MRB would have had opportunity to meet other veterans who actually served with this company. He could have easily learned the name of the company officer in command during 1864. The 37th Mississippi and 54th Alabama fought in many of the same battles. Notice that he doesn't mention anyone else with that company or regiment. I would like to identify the men who witnessed his pension applications to see if any of them belonged to the 37th Mississippi Regt.
Many of the details and actual truth behind the stories will always remain something of a mystery to us.