Read section “b”, kinda clears that up -
Section 13A-11-73Permit to carry pistol in vehicle or concealed on person - Required; possession of unloaded pistol in motor vehicle.
(a) Except on land under his or her control or in his or her own abode or his or her own fixed place of business, no person shall carry a pistol in any vehicle or concealed on or about his or her person without a permit issued under Section 13A-11-75(a)(1) or recognized under Section 13A-11-85.
(b) Except as otherwise prohibited by law, a person legally permitted to possess a pistol, but who does not possess a valid concealed weapon permit, may possess an unloaded pistol in his or her motor vehicle if the pistol is locked in a compartment or container that is in or affixed securely to the vehicle and out of reach of the driver and any passenger in the vehicle.
(Acts 1936, Ex. Sess., No. 82, p. 51; Code 1940, T. 14, §175; Acts 1947, No. 616, p. 463, §3; Acts 1951, No. 784, p. 1378; Acts 1956, 2nd Ex. Sess., No. 43, p. 336; Code 1975, §13-6-153; Act 2013-283, §2.)