All are correct. I have also heard people can legally ship a gun to themselves. Maybe they are going on a trip and want their gun when the get there.
Shipping to yourself (Package addressed to you or In Care Of)
or the FFL returning a gun to you from a Repair (or a replacement for one that could not be repaired) is all legal as there is no Transfer of Ownership of the firearm.
It's that Transfer of Ownership that requires the 4473 & NICS.
Somewhat connected is when a firearm is Consigned for Sale to an FFL..
That firearm is logged in the FFL's book.
If the firearm does not sell, or the orig owner just wants if back before it does sell... That orig owner must go through a 4473 and a NICS check to get that firearm returned to them.
When the gun was left with the FFL on Consignment, it was considered that it's ownership was transfered to the FFL.
I believe pawned firearms are handled the same (02FFL) when the orig owner wants to reclaim the gun.
The return of a replacement firearm will get noted in the Mfg'rs or Dealer/Gunsmiths FFL log book.
The orig firearm coming in, from whom, ect.
If unrepairable, it gets logged out as such and usually marked as 'Destroyed' in the book (or Stripped for Parts and Frame Destroyed).
The Book then shows the replacement firearm info for the above and
the info re when sent back to the orig owner.
So there is a paper trail in the FFL records from one gun to the other and one owner.