Indeed you are correct unless the person doing the ordering has an FFL. You can ship firearm pars, but not the bits that the ATF considers the actual firearm. I got my C&R a while back and can hence get C&R firearms shipped right to my house and skip the gun shop, but I had to get a background check to be able to obtain said license, and last I checked not too many murders were using WWII surplus rifles.
Here's a quote from the ATF's website:
(B7) May a nonlicensee ship a firearm through the U.S. Postal Service?[Back]
A nonlicensee may not transfer a firearm to a non-licensed resident of another State. A nonlicensee may mail a shotgun or rifle to a resident of his or her own State or to a licensee in any State. The Postal Service recommends that long guns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms. Handguns are not mailable. A common or contract carrier must be used to ship a handgun.
[18 U.S.C. 1715, 922(a)(3), 922(a)(5) and 922 (a)(2)(A)]