Hi Chalckwarren, of course your'e right; all sighthounds probably do have a common ancestry, as do ALL breeds of dog.
Mush, I don't know where paid gets his information from regarding the Greyhound, but the Bedu I know, who range from western Arabia to northern Arabia, Jordan, Iraq & Kuwait have probably never seen a Greyhound, let alone introduced it's blood into their Saluki's, which, because of the terrain and climate, would be a backward step anyway.
Cheers.