There are two separate legal issues here.
One is the case which denied the camera owner's claim to copyright, and put the image in the public domain. That is the one involving TechDirt and then Wikipedia.
The other far more absurd case is the one taken by lawyers employed by PETA on the farcical claim that they represent the monkey which pressed the shutter release on the camera, claiming copyright for the monkey. I am mystified as to why the courts have not dismissed that case on the basis that the lawyers have no standing, given that they have no evidence that the monkey wants this case to be pursued by them (or anyone else). That case also wants the owners of web-sites that allow self-publishing to be financially responsible for copyright violations, which could potentially shut down sites like LuLa if people start suing over copyright claims to images posted in forums or on blogs. (Take-down orders might be appropriate in that case, but nothing more.)