Not only that: running the app requires copying it into memory; editing files requires making copies; deploying it to your production servers requires making copies.
I remember that exception, and it was very explicit that you needed to already have obtained copyright permission to use the software. The legal theory behind the "copy to memory" exception is that if a end-user already have been granted permission to use a copyrighted work, then it make sense that they also have permission to "copy" it to their computers memory.
If you have a copyright license that adds a condition to the grant of permission, its hard sell to argue that the exception trumps the condition.
It says, explicitly, that making copies for the purpose of executing it is not an infringement. I do not need permission if it is not an infringing act.
"Notwithstanding the provisions of section 106, it is not an infringement for the "owner" of a copy of a computer program"
If you do not have a licensed permission from the author, you now have to prove that you are the legal owner of the copy. It could be said that they intended to address people who pirated a copy from a torrent site (or a BBS, since this is before the time of torrents), but its a major claim that someone can own a copyrighted work without, 1) purchasing it, 2) having a copyright license to it.
When it comes to GPL in particular, the question is also if the recipient is a owner or a licensee. The license text specifically call "you" to be equivalent with "licensee", which makes the claim of ownership even more dubious.
I don't think acquiring a copy is an act of distribution by the acquirer. Besides, the copy you received while acquiring it was not modified by you, so that would not affect the modified version which was never published. AGPL cannot change the definition of the word publish to be different than that of the U.S. Copyright Code.
You don't own the copyright. You don't have the right to download it on to your hard drive (aka "reproduce the copyrighted work in copies"), except to the extent AGPL allows you to.
Hint: How did you (the developer) originally acquire a _copy_ of the AGPL'd sourcecode?