I think that "picnic lunch" has a meaning far beyond a sandwich and water. We've never been turned away. And it's not something I even worry about. We carry the igloo MaxCold backpack with our cold waters and clif bars and it's fine. Of course we also do eat in the parks. We have our favorites.
Security is on the way from garage to citywalk before the main people mover walkway, as well as on the walking paths from the resorts just before you enter citywalk.