This graph shows two striking things. First, around 2000, the trend for middle-aged U.S. whites - all educational groups combined - stopped going down and started going up. Bound et al. might not say that qualifies as a "dramatic" increase, but it is clearly an increase, and that fact has nothing to do with education selection effects.
Second, and even more importantly, the USW trend post-2000 is markedly, hugely different from the trends for all other countries AND all other racial groups (though U.S. blacks are not displayed on the graph for some reason, Case & Deaton report that their mortality rates have also been trending downward).
This trend difference is far more important than the absolute change in mortality. It means that while good things are happening throughout the developed world that are causing mortality to fall for almost everyone, U.S. whites are being left out of this trend. Geronimus, Harris, and other critics spill a lot of ink over whether the USW trend is really upward or flat, but this distracts from the real issue, which is the big difference between U.S. whites and everyone else in the developed world.