I shared your confusion after reading the Art De Vany interview.
I always do the WOD on an empty stomach; at least 2-3 hours after lunch. This is mostly because, for me, doing the WOD with anything in my stomach other than water, is inviting an unwelcome return of that partially digested lunch.
As for post-workout nutrition, most of what I've points to the consumption of sufficient (usually simple) carbohydates and protein. You'll most likely find endless different definitions of what "sufficient" means.
I have a protein shake immediately after each WOD; skim milk + protein powder and swallow fish oil capsules with it, to keep it Zone-friendly. After some WODs, that is pretty much all I'd be able to keep down.