I get an edgemesh site to accept file A (perhaps the site allows me to upload a user avatar, upload an image on a forum, etc). I then behave as a node in the mesh, and receive file A. When I get a request to replicate file A to someone else, I send them file A', they check the MD5 hash, and the hash matches. Not seeing how that doesn't work?
It is admittedly a narrow attack, but I think it works.