OK so it turns out I am wrong here! Cool.

I have it upside down/diametrically wrong, however you see fit. Right that structures exist, exactly wrong on how they apply.

It is registration that guarantees access to statutory damages:

https://www.justia.com/intellectual-property/copyright/infri...

Without registration you still have your natural copyright, but you would have to try to recover the profits made by the infringer.

Which does sound like more of an uphill struggle for The Intercept, because OpenAI could maybe just say "anything we earn from this is de minimis considering how much errr similar material is errrr in the training set"

Oh man it's going to take a long time for me to get my brain to accept this truth over what I'd always understood.