It's a little be more complected than this, since the FLL is taking a 80% receiver, and turning it into a 100% receiver isntead.
Since turning a 80% receiver into a 100% receiver constitutes building a firearm, the FLL needs to have a sot 7.

Also, since it now its a completed firearm that he is sending back out, the firearm has to be paperworked  back to the owner now.

If the FLL is out of state, then it needs to be sent to a FLL in state, who will do the paper work to transfer the complete firearm into ownership of the person that sent him the parts to turn into a completed firearm.

To bottom line it, you can build a type 1 completed firearm for your own personal use without needing any paperwork for it.
The moment that it being completed by someone else, it has to be registered as first a completed firearm, then paper worked back to the person that sent the parts.  And if you where wondering, having someone build your parts kit into a firearm for you that does not have a FFl SOT 7, does run into some problems, since production of a Firearm  not for personal use only,  requires a FFL SOT7 licenses.

As for the receiver being a 100% complete receiver that was paper worked to you to being with, although it may be sent directly back to you once completed, but since there was no completed Firearms Excise Tax collected when you bought just the receiver, this needs to be collected once the firearm is completed, and again, your back to the catch 22, that's if a FLL is going to produce firearms (even from just a registered receiver), he needs to have a sot7.  Again, a FFL type 1 is only for sales and repairs of firearms, not to produce them isntead.