No, they refuse to delete the photo because animals can't own copyright, and they contend that the monkey took the picture, so it's not the photographer's copyright either, so no one has copyright to it.
IMO a court will side with the photographer. If I dropped my camera, and whilst rolling down a hill it took a stunning photograph, it would be my photograph. The monkey isn't contesting his copyright claim, and I doubt that the copyright of a photograph depends upon something as specific as holding the camera and controlling the shutter. Giving non-human primates your camera to take pictures could be a photographic method.
I kind of agree with this. The argument is a bit fallacious and to be honest, unless the institution itself fights for ownership, a monkey owning anything is a bit ridiculous. There are interesting arguments for animal proprietorship in wills, but this is meh at best.
I am willing to split the difference with you
Old world monkeys and apes form their own clade and calling the whole place Old World Monkeys is not uncommon either is your usage. Although going by noses alone I am right.
Thanks for sharing the article! Haven't seen the pictures so far, they're great, and the problem those guys are facing are very interesting, especially with the recent debates in mind regarding animal rights I read recently.