I'm aware you didn't "propose" it as a defense, but that's how it would work in a litigation.
>if AI eventually produces content indistinguishable from what humans can produce, what prevents these foreign outsourcing businesses from quietly pretending they still hire humans?
The fact that they don't and if it is discovered, it will mean all of the work generated by them is not copyrightable and therefore everyone is free to copy it. They'd also have to lie to the copyright office and the businesses they were selling their services. The only thing doing the work here is the lie.
Right now I can go to another place and find another photographer who will recreate something for less. Technology might make that more trivial, but it doesn't change the fact that as a business opportunity it'd only work by having to massively misrepresent oneself.
Ostensibly, if I was a business and I was contracting these kinds of services, one thing guaranteed to be in the contract would be a clause that they authored the works, obtained the copyrights, etc, lawfully. And generally in a contract they would represent what the business represents (we are an illustration shop that sells images that we authored... etc).
So to more specifically answer your question - "what would stop them?" the same exact repercussions as would right now (which is what I intended to make clear in my initial response to you).