Not strictly vegetarian, to clarify. From my reading of Weston Price's quotes, to his credit he did not recommend, as Fallon and Enig do, a high fat, high protein diet. On the contrary, he recommended a vegetarian-based diet. If he didn't recommend that, then he was wrong too, but I think he did.
But you don't have to be a history major or researcher to know that all of the thin populations lived (and still live) on a vegetarian-based diet -- rice, potatoes, and corn -- the three things that the low carb gurus say we should avoid.
A picture's worth a thousand words and there's no denying that Fallon and Cordain (paleo founder) are fat and look ill. That should be enough warning, I would think.