Since this is a Federal law....
Since this is a Federal law I'm sure that you are right. However, I'm perusing our state laws to find whatever language that I read in the past to base that on. Unless I do, I'll go with your answer.
UPDATE: Ok, I found the laws and copied them verbatim. You are right, simply possessing a sawed off shotgun is breaking the law.
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SECTION 16-23-220. Unlawful transportation of machine gun, military firearm, or sawed off shotgun or rifle within State.
It is unlawful for a person to transport from one place to another in this State or for any railroad company, express company, or other common carrier or any officer, agent, or employee of any of them or other person acting in their behalf knowingly to ship or to transport from one place to another in this State a machine gun or firearm commonly known as a machine gun, military firearm, sawed off shotgun, or sawed off rifle, except as provided in Sections 16 23 250 and 23 31 330.
A person who violates the provisions of this section, upon conviction, must be punished pursuant to Section 16-23-260.
SECTION 16-23-230. Unlawful storing, keeping, or possessing of machine gun, military firearm, or sawed off shotgun or rifle.
It is unlawful for a person to store, keep, possess, or have in possession or permit another to store, keep, possess, or have in possession a machine gun or firearm commonly known as a machine gun, military firearm, sawed off shotgun, or sawed off rifle, except as provided in Sections 16 23 250 and 23 31 330.
A person who violates the provisions of this section, upon conviction, must be punished pursuant to Section 16-23-260.
SECTION 16-23-240. Unlawful sale, rental, or giving away of machine gun, military firearm, or sawed off shotgun or rifle; exceptions.
It is unlawful for a person to sell, rent, give away, or participate in any manner, directly or indirectly, in the sale, renting, giving away, or otherwise disposing of a machine gun, or firearm commonly known as a machine gun, military firearm, sawed off shotgun, or sawed off rifle, except as provided in Sections 16 23 250 and 23 31 330.
A person who violates the provisions of this section, upon conviction, must be punished pursuant to Section 16-23-260.
SECTION 16-23-250. Exceptions to application of article.
The provisions of this article do not apply to the Army, Navy, or Air Force of the United States, the National Guard, and organizations authorized by law to purchase or receive machine guns, military firearms, or sawed off shotguns or sawed off rifles, from the United States or from this State and the members of these organizations. Any peace officer of the State or of a county or other political subdivision, state constable, member of the highway patrol, railway policeman or warden, superintendent, head keeper or deputy of a state prison, correction facility, workhouse, county jail, city jail, or other institution for the detention of persons convicted or accused of crime or held as witnesses in criminal cases or persons on duty in the postal service of the United States or a common carrier while transporting direct to a police department, military, or naval organization or person authorized by law to possess or use a machine gun, or sawed off shotgun, or sawed off rifle, may possess machine guns, or sawed off shotguns, or sawed off rifles, when required in the performance of their duties. The provisions of this section must not be construed to apply to machine guns, or sawed off shotguns, or sawed off rifles kept for display as relics and which are rendered harmless and not usable.
The provisions of this article do not apply to any manufacturer of machine guns or military firearms licensed pursuant to the provisions of 18 U. S. C. Section 921 et seq., any person authorized to possess these weapons by the United States Department of the Treasury, the Bureau of Alcohol, Tobacco and Firearms, or any other federal agency empowered to grant this authorization, any common or contract carrier transporting or shipping any machine gun or military firearm to or from the manufacturer if the transportation or shipment is not prohibited by federal law, or persons licensed pursuant to Section 23-31-370.