> So If I set up a camera that has an infra-red trigger that is set off by an animal,
Then you're fine because you have set up and targeted the camera, you have framed the shot as you want it to be. It's your copyright creation.
In this particular and highly unusual case this did not happen. The photographer did not frame the shot or have any real creative input into how the shot would come out. He even claimed it was a lucky accident. As such, his involvement in creating the shot was pretty much limited to a) being in the right place at the right time and b) having the camera set up to take shots at the right exposure levels, etc - but as it was clearly set to autofocus and probably at least on either automatic exposure or automatic aperture setting (but none of us can tell that without the exif data) his argument for creative input on this is pretty week.
Similarly, if you and your family are on holiday and ask a stranger to take your photo, you still tend to own copyright of the photo because the assumption is that you are setting up the shot yourself, you are in control of where you and your family stand and the stranger is little more than a 'meat tripod'. This is where that differs from hiring a professional photographer to take your family photo.
The monkey example would be a bit analogous to you being on holiday, leave your camera on the table, someone runs up, takes your camera, takes a photo of themselves, and runs away. You wouldn't own the copyright in that case either. But then you'd probably just delete that picture (or pass it to the police!)