Shakespeare's Long Lost Cousin

So there's a story going around about Reverend Shakespeare, who claims to be the closest living relative to you know who. I was under the impression that there were no descendants of Shakespeare, and we discussed this back in 2007. So, what gives?

He claims to be descended from Shakespeare's first cousin, John Let's talk about that, first. To be Shakespeare's cousin means that this John would have to have been the child of one of Shakespeare's brothers or sisters, right? Technically if he's telling us that the Shakespeare family name has continued all the way back, that would even rule out Shakespeare's sister (Joan), who would have had her name changed.

I actually just found this genealogy page that goes into the details of how the ancestry lays out. I'm not yet sure I believe it.

What do you think? And, is this interesting? I'm torn. It's not like you can lay any claim to his poetic genius - I don't recall brother Gilbert or Edmond banging out any masterpieces in their day. But, still, if proven it's be kind of cool to be a walking connection to history like that.