The point is that something as obscure as a statistical adjustment, driven by a seemingly trivial shift of 5 months in average age in a 10-year window, is enough to completely change our story.
Let me emphasize that this is all in no way a “debunking” of the Case and Deaton paper. Their main result is the comparison to other countries, and that holds up just fine. The place where everyone is confused is about the shape of the trend among middle-aged non-Hispanic white Americans.
The story being told is that there was something special going on, with an increase in mortality in the 45–54 age group. Actually what we see is an increasing mortality among white women aged 52 and younger—with nothing special about the 45–54 group—and nothing much consistently going on among men. Now that we have the facts down, the explanations can follow. And there is much more work to be done, in particular in integrating these data with what we know about “cohort effects”—behaviors that different generations carry through their lives.