If you are building with a rear hatch (or even a boxy barn door rear), you will probably want some sort of arched (or deeper than a standard stick built) header near the top. A jamb or sill across the bottom, if that doesn't hinder access to the load deck for your purpose, would also be helpful to make the opening in "the box" more rigid. You might even consider a full perimeter frame around the hatch opening. I forget who it was that uses RV trim molding with inserts to seal their surface mounted hatches (maybe someone else knows who/what I'm talking about). Again, this might be a necessary compromise between stiffening and ease of access, but if you are lacking a rear bulkhead and don't have enough stability in the door seal area you are sure to get leaks.
On my hybrid foamie I have a Benroy like rear hatch. My walls are 1-1/2 thick foam, 5mm Okoume marine ply inner skins, with 2-plies of 6oz FG/epoxy outer skin. To make a hard edge on the galley walls, I laminated bent slats of fir in the the arch shape of the profile and embedded those into the wall edge before skinning. I only extended the hard edge 8 inches or so forward of the 2x2 oak hinge spar, but if I had it to do over I would have sent it forward at least as far as the next roof spar (again, hybrid foam construction... YMMV). My point is, even with all of that extra non-traditional foamie structure, a floor to roof vertical bulkhead immediately behind my hinge spar, and inner rear cabinet unitized space frame, I am still able to flex the open ends of my walls a tiny bit. I'm not worried about this going down the road because my hatch is very solid (...and heavy...

), and with beefy draw latches will lock into the seal to hold everything firmly, but I only left a scant 1/4 inch gap between inner wall skins and my outer hatch ribs, so anything more than a tiny little bit of flex would have been unacceptable (the ribs would have rubbed the finish off of the walls and/or the edges of the hatch would not sit flush enough to the faces of the walls for my liking. I'm not saying you should adopt my build techniques or materials, by far. I'm just saying that it isn't so much the materials we use, but the structural composition, geometry and joinery of the structure that determines if something will be floppy or not. Relatively thin panels, wall edges or even trailer frames, will flex. They will, but the deeper you make a supporting header, jamb, or surrounding frame, the more gusseting effect you will get. Like shear panels in home construction, triangulation is key. It's not just the load bearing walls that hold your house up.