The issue is transfer of ownership. If no transfer of ownership, does not need a FFL.
For RIFLES and SHOTGUNS- they can be mailed by US Mail by a private citizen. Be certain they are not loaded. HANDGUNS may not be mailed except by a Dealer or Manufacturer.
In the case of a firearm sent for service, it can be returned directly to the owner without going thru a dealer- no transfer of ownership. The Mfgr can also say "Sorry your gun broke- it is under warranty- here is a new gun of the same type." THAT does not need a FFL either.
18 US Code, section 922. Long, dry read, but it is tucked in there.