What's the correct theory, logic, and anthropology context? I'd like a bit more detail.
I've been following the development of these ideas for a long time at GHMB--followed links--and I've appreciated the way Graham has promoted and presented about Gobekli Tepe.
Statistics is something I teach--as well as research design--and I have a rudimentary understanding of precession. I expect Swearington's book to be highly speculative, so it would take a great deal of nonsense before I would get discouraged.
I would expect almost anyone to successfully debunk these claims--or any other claims. We're still at the blue sky thinking stage of thinking about Gobekli Tepe.