I haven't read Silver's book, but I do understand Bayesian probabiliy. (And I'm a big fan of it.)
I think the author of this article falls into the trap of forgetting that Silver is writing for the masses in the same way the writer of Freakonomics was. People attacked Freakonomics too for similar reasons (broad conclusions, some misleading details, etc). What critics need to keep in mind is that the book wouldn't sell if Silver bored America with too many explanations for statements that are, in the end, small and correct enough that we can take his word for them.
Silver seems to be using “Bayesian” not to mean the use of Bayes’s theorem but, rather, the general strategy of combining many different kinds of information.
Yes, and? That's entirely valid enough to be included in his book.