If the pictures are hosted on sites like rotten.com, ogrish.com and consumptionjunction, why can't the mods just block all images from those sites?
Because it is your browser that assembles the page, not FR.
You can block those images and sites with Firefox or Mozilla as your browser (could probably be done with certain settings in Internet Explorer) or you could block those sites out completely with entries in your computer's "hosts" file. The downside to the "hosts" approach is that if the rat uses an IP address instead of a host name for loading the image you would have to rely on your browser to block the image. It's all pretty technical, but you can find sites out there that provide decent help with those kinds of settings.
The pictures are public domain. They are all over the web. If a person happen to stumble upon this picture while reading FR, he can use the image URL and post it somewhere else before the mods nuke the pic. Also, he can save it into his computer and upload it to a photo hosting site and use it.
In this manner the pics could have even originated from FR!