I think we could be missing an important point.
The top 20% of households earn about half of the income.
Their behavior has a much larger impact on the national savings rate than the behavior of the bottom 80%.
Moreover, unemployment benefits provide a much larger share of one's income for the bottom 80% than it does for the top 20%. And the top 20% is far less likely to lose their jobs in this recession compared to the bottom 80%.
The previous models were assuming perfect income equality which is obviously not the case.
If a person earning $200,000 a year goes from saving $40,000 to saving $80,000, that can swamp the impact of a few unemployed construction workers.
One of the biggest shifts, in my opinion, is the huge reduction in NEW consumer debt. Credit cards are being cut off. Middle/Working class people can't get access to new loans. Instead of spending 110% of their income, they are spending 100%. That also has a big impact on the savings rate.
If a $50K/year person goes from spending $55K to spending $50K, society has $5,000 less debt. Put another way, society has $5,000 more savings. Why shouldn't we count this as new savings? A decline in borrowing has the same net effect on society as an increase in savings. If I earn another $100 at work or my bills drop by $100, my standard of living improves by the same amount regardless of the reason.

Consumer debt, which had been growing rapidly, has stalled out.
We added roughly a trillion dollars a year in new consumer debt each year between 2002 and 2008. Now we aren't adding any new net consumer debt.
Households are rebuilding their balance sheets.