How do I install hanging cabinets with a flimsy backing?
I was just looking at the site you mentioned in your question. Definitely  factful, but not the best DIY tutorial, and leaves out many alternative methods. I have always preferred to mount cabinets through the backer above the top panel of the cabinet so the mounting screws do not show inside the cabinet. Even cabinets with a thin flimsy back panel can be successfully hung to the studs if you interlock the jams with cabinet screws( clamp the cabinets together and install a 1 1/4 inch counter sunk cabinet screw through the jam to secure it to adjacent jam) and then use a screw that has a washer mounded right to it, Yes, a special cabinet mounting screw, to secure cabinet to the wall at each stud. There is usually about 1 to 1 1/2 inches of some sort of frame or panel extending above and below the box area of the cabinet. This area top and bottom is the best place to install the screws.  Another method is to install a good looking ledger level under the cabinets for them to rest on, taking most of the load away from the screws holding the cabinets to the wall.  There are some great how to videos on the "This Old House" web site, check them out.