OK, I've had a bit of a play with the scene and it appears as though the bone influences for the inner bones are affecting the flow of the object.
If you set limited range on for all the bones, then adjust the influence spheres to appropriate sizes, you will see differing results with the overall shape of the box. I found the best results by setting the influence range to 1mm for each of the vertical bones and 1m for each of the horizontal bones. This way, the vertical chain only has influence over the overall shape of the bone sub-chain. The main horizontal bones are the ones controlling the deformation of the box.
Attached is an updated scene and object file for you to take a look at. Note also that if you set the subdivison options for the box to 'after bones' then the problem also disappears, but the box does not appear to actually subdivide correctly and instead maintains a distinctly angular feel.
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