A FFL is not required to ship a long gun. No need for a 1508 since it is not necessary to provide proof of having a FFL. A FFL is required to mail a handgun. Only reason to provide a 1508 is to ship a handgun. The last link you provided does mention a 1508 being required to ship a handgun.
I never said it was required, but he did tell them he was also an FFL, which may have caused the confuaion
The top of Form 1508 says it may only be used by FFL's
I did miss the one referrence to the form among all the regulations on the second link