That argument works just as well for camera rental companies. Because that's all he did in the end - lend the camera to a different kind of ape.
Who would own the copyright had it been another human who pressed the button?
- One human sets up the camera -- another frames the shot and takes the shot.
I would say the second human who framed and shot the image is the copyright holder... meaning the monkey would own the copyright had the monkey been human... but since the monkey is not human (and copyright only applies to humans), then it's public domain.
We're not talking about a monkey (or human) framing and taking photos. We're talking about a monkey pressing a button because it makes an interesting sound. There is no authorship there.
Then why are we assigning authorship to a human? Just because he happened to be there?
(Also, I can make a song on a guitar without knowing what it is nor how to play it -- I still hold copyright over my work).
Since the entity framing the shot and pressing the button is the monkey, but non-human animals can't own a copyright, no copyright is generated.
It routinely explodes people's heads that copyright law works like it actually works, not like people wish it did.
The situation is a lot more analogous to a celebrity inadvertently taking a selfie in a scuffle with a paparazzo; the celebrity is the intended object of interest and inadvertently triggers a composition far more interesting than the paparazzo's original concept, but the paparazzo was there with the intent of making a creative work. I'm not sure whether any sort of legal precedent exists for that, but I'd be surprised if legal arguments the paparazzo was too creatively uninvolved to have any say in the image distribution rights were positively received.