In this case, the monkey "borrowed" somebody else's camera, without permission, and took the picture in question. If I steal somebody's camera, and take photos with it, do I still own the copyright?
Generally, yes, unless your work contract says something else. There are many companies who only have such work contracts, but there are counter examples.
Your downvotes suggest primate logic hard at work. You asked a question. Primates decided it must be rhetorical, and that you must mean you don't (or do), and that whichever you meant, your stance (though not voiced) must be disagreed with — downvote!
If i break into someone's apartment and write a poem with their pen and paper, obviously i still own the copyright.
However, if i write code for an employer the contract almost certainly states that the employer owns my work (and in some (all?) states it's a Work for Hire). jrockway was purposefully making an argument that does not apply in the situation or make sense, and he is being downvoted for it.
I do not appriciate ad hominem attack against those that downvoted a trollish comment.