Actually I can imagine his story might have some merit to it. In 1865 Sherman had already gone through Atlanta and many units were put together piecemeal to deal with on-going events. Since the government of Georgia was in turmoil I imagine many of these units were never recorded.

On April 15, 1865 all Georgia units were ordered to Columbus Georgia to defend it from Union General J.H. Wilson's Cavalry command, although Columbus surrendered to Union General J. H. Wilson on April 16, 1865.

I find one Captain Cromwell listed and it's interesting that the company he was Captain of was from Muscogee County which Columbus is in:

Company F (Muscogee County), 3RD Regiment Georgia Infantry Reserves
Capt. Oliver Cromwell

Another interesing thing is there was a Private J. A. Adams in Company C of the same regiment but Company C was from Bibb County which Macon is in.