Since the 7th Alabama already had a Mobile Depot flag, it would make sense that the additional "Aberdeen" flag would go to the Alabama escort company. It also explains how Captain Storrs came by the flag that now resides at the ADAH. As quoted below from the ADAH provenance reconstruction, it may explain why his account is somewhat less specific than Rucker's.
He and his men were not present when Rucker received the flag.
According to an account attributed to Colonel E. W. Rucker, this flag was presented to his brigade by Mrs. Lorenzo Leedy, a widow of Aberdeen, Mississippi. The flag was made from Mrs. Leedy's wedding dress by the ladies of Aberdeen. Former Captain C. P. Storrs, (Co. F, 7th Alabama Cavalry) reported that some of the "patriotic ladies" also contributed material from "their best dresses" in order to make the flag. Storrs further stated that the flag was presented in 1863 during one of the Tennessee campaigns and at that time, his company was selected as the escort and color company. Captain Storrs' company continued to carry the flag until the end of the war. The last flag bearer was F. C. Gregory of Montgomery. The flag was preserved after the war by Captain Storrs who donated it to the Alabama Department of Archives and History on July 8, 1907.
The image below is that of Lieut. Col. William A. Dawson, 15th Tennessee Cavalry, killed Nov. 24, 1864, near Columbia, Tenn. --
http://www.historicalshop.com/sitecontents/confederate/images/dawson.htm
James Dinkins, Personal Recollections and Experiences in the Confederate Army, 1861 to 1865, formerly an officer of Co. "C", 18th Mississippi Cavalry, page 225 --
The following morning, Rucker again took the advance, and caught the rear of the enemy about half way between Mount Pleasant and Columbia. He drove them beyond a creek near Columbia, where they took cover behind breastworks. In the last charge on that day, November 24th, Colonel W. A. Dawson was killed. We saw his body lying beside the pike as we followed Rucker. He was a gallant officer.