I think this is a bit of a myopic take. It's like saying it's my property I can do what I want, yet there exists designated historic homes or neighborhoods that are deemed to have cultural value where modifications do in fact need to be approved.
I'm with you on the "rare" part. If people are thinking about 70+ year old documents or ancient manuscripts, I doubt that's what AI is being trained on and is being destroyed, but it's reasonable that people find _that_ idea distasteful.
You can say it's manufactured but if these companies ignore this criticism, it's just another way AI companies are committed to losing the public.