Both, the monkey and the camera are "ownable" and took part in creating the picture... I would even go as far as to argue the monkey was more important than the camera. Should we also give copyright to the "owners" of the algorithms that took part in calculating the correct exposure for the photographs the monkey took?
And it's not like trap photography in that the monkey framed the picture himself, and framing is in itself a very important part of photography. Some would say even more than exposure that can (and was in this case, as I already pointed out) automated by the camera.
EDIT: redaction.