...it's the lower receiver that he fabricated; the lower receiver is the part with the stamped- or machined-in serial number that has to be bought from a licensed firearms dealer and recorded as such in order to be legal. All the other parts can be obtained fairly easily and without traceable documentation.
Essentially, for legal purposes the lower receiver =is= the gun."
A firearm needs a serial number in order to be transfered. It is perfectly legal to build your own firearm without a serial number so long as you did not intend to transfer it when it was built. If you later change your mind you can add a serial number and then transfer it. It does not need to be bought from a dealer in order to be legal if you made it yourself.
You are correct in that the lower is the "gun"
Hypothetical question ahead: I ask this question though, what happens when ATF changes it's mind about where they want the serial number. For example if they had first said that the serial number had to be on the uppers, then later changed their mind and decreed that the serial had to be on the lower...