Wikipedia is being disingenuous and immature here. I would be very surprised to see a court agree with their argument.
Courts generally try to avoid reaching perverse results that undermine the purpose of the laws they're enforcing. Copyright exists to support the kind of work that Slater was doing.
...and asserting that images accidentally created by non-human animals belong to the public domain undermines copyright how, exactly? I'm not seeing much of a slippery slope here.
Copyright exists to incentivize creativity. The fact that we're arguing about this proves that there's at least one photographer that would be disincentivized by your proposed rule.
This also happens more than you might think. See the video of a lion stealing a wildlife photographer's Go Pro video camera, for example (http://gizmodo.com/5805961/lion-steals-and-chomps-on-gopro-w...). If wildlife photographers know that they can keep copyright in such situations, that will incentivize wildlife photography generally (at the margin), and these kinds of pictures/videos specifically. The world will be that much more awesome.
I see no reason why "letting a monkey play with my camera" should be less of a creative act by a photographer than "clicking the shutter button". Artists have done much weirder things.
A rule based on incentivizing photographers will give Slater the copyright here. Whereas a rule based on the hair splitting advocated by Wikipedia would cast doubt on the copyrightability of all kinds of creativity that rely on an element of randomness or non-human actors (e.g. animals, the wind, sunlight, /dev/urandom).
Courts generally try to avoid reaching perverse results that undermine the purpose of the laws they're enforcing. Copyright exists to support the kind of work that Slater was doing.