Sprawl IS a new phenomenon, though. We didn't see the kind of suburban sprawl that we see today until after WW2, when cars became THE way to get around. It became more and more dominant and entrenched as the interstate highway system developed.
Remember, we're talking about relative density within a metro area, not how close each metro area is to the others. If you look at cities that were more or less fully developed prior to WW2, like Boston, you find that they're more compact, as opposed to, say, LA or Phoenix.
That said, I don't think it's the only thing making us fat. But I do think it's one contributing factor.