After the Battle of Nashville, Hood’s Army retreated toward Alabama.

From Rowland's capsule history.

The 22nd was "at Columbia, December 20, Featherston's Brigade was one of the seven selected for Walthall to command as the rear guard of infantry, remaining in face of the enemy until the rest of the army had gained two days’ start. December 21 the brigade was reported 727 aggregate, the Twenty-second, 104."
My notes from research on the 7th Mississippi and Lee’s Corp:
On December 18th “Lee’s rear guard along with Buford’s Cavalry held the federals of Wilson’s cavalry while Stewart and Cheatham crossed the Harpeth River at Franklin and then burned the railroad bridge after they crossed. Wilson was able to ford the Harpeth and again Lee’s men made a stand across the pike at Winstead and Breezy Hills, where they suffered heavy losses including Lee who was wounded and gave up command to C.L. Stevenson who was successful in delaying Wilson long enough for Stewart and Cheatham to evacuate Spring Hill.
Cheatham took over rear guard and held off the pursuers in a skirmish south of Spring Hill and then crossed the Rutherford Creek. The army bivouacked between there and the Duck River and Hood established his HQ at Columbia. Forrest arrived that evening.”

Since the muster roll was made on the 21st, Rayburn could have been captured while en-route to Columbia between the 18th and 21st and listed as captured on the 21st roster. Looks like Cheatham's rear guard action south of Spring Hill fits the scenario described in the man's records.