Well, these are the federal law codes that they (ATF, NRA, and several shipping services) cite, Federal Law 18 USC 922(e), and 27 CFR 47831(a) quoted below.

The NRA plainly and clearly states (with no muckity-muck "lawyer-ese" language) on their website:
MODERN LONG GUN to a licensed FFL DEALER: May use U.S. Post Office or a common carrier. Carrier must be notified that the package contains a firearm.

I'm no lawyer, but I'd like to think the NRA knows what advice they're giving about shipping a firearm......

https://www.law.cornell.edu/uscode/text/18/922

https://www.law.cornell.edu/cfr/text/27/478.31

Quote

922. Unlawful acts

(a) It shall be unlawful --

(2) for any importer, manufacturer, dealer, or collector licensed under the provisions of this chapter to ship or transport in interstate or foreign commerce any firearm to any person other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector, except that --

(A) this paragraph and subsection (b)(3) shall not be held to preclude a licensed importer, licensed manufacturer, licensed dealer, or licensed collector from returning a firearm or replacement firearm of the same kind and type to a person from whom it was received; and this paragraph shall not be held to preclude an individual from mailing a firearm owned in compliance with Federal, State, and local law to a licensed importer, licensed manufacturer, licensed dealer, or licensed collector;

(e) It shall be unlawful for any person knowingly to deliver or cause to be delivered to any common or contract carrier for transportation or shipment in interstate or foreign commerce, to persons other than licensed importers, licensed manufacturers, licensed dealers, or licensed collectors, any package or other container in which there is any firearm or ammunition without written notice to the carrier that such firearm or ammunition is being transported or shipped; except that any passenger who owns or legally possesses a firearm or ammunition being transported aboard any common or contract carrier for movement with the passenger in interstate or foreign commerce may deliver said firearm or ammunition into the custody of the pilot, captain, conductor or operator of such common or contract carrier for the duration of the trip without violating any of the provisions of this chapter. No common or contract carrier shall require or cause any label, tag, or other written notice to be placed on the outside of any package, luggage, or other container that such package, luggage, or other container contains a firearm.


Quote
§ 478.31 Delivery by common or contract carrier.
(a) No person shall knowingly deliver or cause to be delivered to any common or contract carrier for transportation or shipment in interstate or foreign commerce to any person other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector, any package or other container in which there is any firearm or ammunition without written notice to the carrier that such firearm or ammunition is being transported or shipped: Provided, That any passenger who owns or legally possesses a firearm or ammunition being transported aboard any common or contract carrier for movement with the passenger in interstate or foreign commerce may deliver said firearm or ammunition into the custody of the pilot, captain, conductor or operator of such common or contract carrier for the duration of that trip without violating any provision of this part.

(b) No common or contract carrier shall require or cause any label, tag, or other written notice to be placed on the outside of any package, luggage, or other container indicating that such package, luggage, or other container contains a firearm.

(c) No common or contract carrier shall transport or deliver in interstate or foreign commerce any firearm or ammunition with knowledge or reasonable cause to believe that the shipment, transportation, or receipt thereof would be in violation of any provision of this part: Provided, however, That the provisions of this paragraph shall not apply in respect to the transportation of firearms or ammunition in in-bond shipment under Customs laws and regulations.

(d) No common or contract carrier shall knowingly deliver in interstate or foreign commerce any firearm without obtaining written acknowledgement of receipt from the recipient of the package or other container in which there is a firearm: Provided, That this paragraph shall not apply with respect to the return of a firearm to a passenger who places firearms in the carrier's custody for the duration of the trip.

Last edited by BlackFrog; 01/10/17.