I'm trying to get an image taken from the Peach Project and post it on a wikia site and the site that I've posted it on requires permission from the Copyright owners before I can use it. Do I have to have permission to use it?

Yes, you have the permission to use images posted on the peach website. Check the text at the top of this page, it has details about the copyright:
http://peach.blender.org/index.php/about/