Maybe it's easy to say but it feels more like a cultural problem than a technical/procedural one. Why the fuck did they let this happen in the first place? Where is this mentality that even the backside of a cabinet should be build well?
Pride in quality of work? Why does the backside have to be be NOT built well? I hate crappy pressed wood furniture, but the same piece of furniture built by real craftsman using real materials raises the price from ~$250 to over $1200. Admittedly, apples and oranges, but the point is valid.