Thanks for your comments. I have to admit you might be onto something with these societies spreading stories about each other to throw us off the scent. It makes perfect sense, as we don't actually know much about these groups anyway and any info given to us is usually lapped up by people myself included.
I wasn't looking for a difinitive answer as you said these groups are secretive so we'll probably not find out. But I did want to get a debate started and speaking to people like you and hearing theories like yours is what I wanted.
Check this link out: The Weaver Code: an ancient mystery solved by John W Balfour
It's about one of the groups I've mentioned, not much is known about them and maybe this guy is part of another group to try and deflect info from his group. Have a look and let me know what you think.