I think the thing that puzzled everyone, was: if it's not genuine then how the hell was it created (painting has pretty much been ruled out) and who in the days before photography would have wanted to create a negative image?
A while ago, however, I watched a programme on TV which suggested it could have been done by the camera obscura method (pinhole camera) I can't remember now exactly how it worked but the programme showed the method and suggested the 'culprit' was probably Leonardo da Vinci.
One of the arguments against it's being genuine is that if the cloth had been wrapped around the face, the features would have looked much broader when the cloth was unwrapped and spread out.
