Well, no. He didn't say that. He gave the primality of 11 as an example of a mathematical truth, and then went on to say that the truth of some mathematical statements is undecidable.
I do disagree with Davies, however, that Gödel's theorem has anything to do with physics. Gödel's theorem only applies to certain types of formal systems. It is by no means clear that there exists no formal system appropriate for describing physics that is free from undecidable propositions. Furthermore, if even if all appropriate systems suffer this blind spot, it isn't clear that it would conceal anything important about the universe.
It seems intuitively clear to me if you make the assumption that people (i.e. beings capable of formulating number theory) are a natural consequence of physical law.
I'll grant you what's not clear is whether the incompleteness theorem has anything interesting to do with physics.
IMO, this is a very, very horrible way to get the idea across. For starters, it's flat out false. It makes the claim in an even more positive fashion than I put it, and is just going to end up confusing a lot of people, despite his rather insufficient attempt later to correct himself. I do agree with everything else you've said, Physicist -- no argument there -- but I guess I just don't think it's a good idea to make false statments, as he's done here. It only adds to the confusion, skepticism and ignorance. We can almost guarantee there are going to be people running around after reading this article claiming that math is a joke, very likely including NEA types who think there are no "right" answers anyway.