However, until very recently the creative product must have been created by someone so there is an implicitly created copyright over the product in the first place. With AI output, that might not continue to be true, we don't really know how it'll work out yet.

In any case, the corporation did not create the product, people created it and their contractual relationship with the corporation defined how the ownership of that work was managed. So, I don't find it too unusual that this element of personhood is available to corporations.