The key point is that aggregate spending decline (and the economy officially entered a recession) before the financial crisis happened. So there is a problem with the timeline if the financial crisis really caused the recession.
Mian and Sufi's story is that the decline in spending really came about because over-leveraged households had no choice but to drastically cut back on spending when home values declined, and that underwater homeowners and those facing foreclosures were most affected, a simple point that they illustrate with basic math.
This story is related to, but somewhat in tension with, the narrative favored by proponents of market monetarism, who would say that the recession and banking crisis were caused not by the housing crash forcing homeowners to cut spending, but more proximately by the Federal Reserve allowing nominal gross domestic product expectations to fall drastically, which in turn led consumers and businesses to pull back.
The Mian and Sufi analysis doesn't necessarily contradict that line of thinking, but it also places less emphasis on monetary policy than other accounts of business cycles. As I mentioned in the Washington Examiner, it instead highlights the importance of leverage both as an indicator of the business cycle and as a potential policy target. That is related to the work of John Geanakoplos