Why were the measured productivity gains so high in 2009?

You'll find the BLS statistics here, with a broader list of tables here.  For the "Business Sector, output per hour," 2008 shows an overall growth rate of 1.1 percent.

The quarters of 2009 yield 6.1, 7.2, 8.3, and 3.5 percent growth rates.

The quarters of 2010 show 3.5 and 1.1 percent growth rates.

Total hours worked are falling through 2008 and falling at more than five percent by the third quarter of 2008.

In other words, there was a lot of "productivity growth" precisely when workers were being laid off, and not so much before or after.  I interpret the "high productivity innovation" as the decision to lay the workers off, and the selection of workers, not the sudden advent and withdrawal of some new high productivity technology.