This is a popular misconception by bloggers: they think that they have the right to copy anyone’s art, just because they found it on the internet, which is very far from the truth. The copyright stays with the creator, no matter who published it on the net, unless the copyright owner has sold the rights outright.
Did Slater offer a banana in exchange of the camera, one wonders?!
Evidently, copyright law isn’t totally up-to-date when it comes to pictures taken by machines (like a camera onboard a RC plane), animals, or whatever.
There have been many cases of animals, like gulls carrying off GoPros, that unknown to the thief have recorded the event. Who owns the copyright of such an image?!
In the case of the monkey, it is evident that he/she has an understanding what he’s doing, thus is the photographer. An elephant, triggering a trail camera, can hardly be called a photographer, but who owns the copyright?!

Started out doing photography at the age of 6 using an uncle's old 1940 kodak brownie box camera. At 15 years of age, I decided to buy my very own 1975 Praktica SLR camera. I now shoot with a Nikon D850. I do unpaid TFP and commercial paid work.