What was done
In the words of the authors, "net primary productivity (NPP) in North America was computed for the years 1982-1998 using the Carnegie-Ames-Stanford approach (CASA) carbon cycle model ... driven by a new, corrected satellite record of the normalized difference vegetation index at 8-km spatial resolution."

What was learned
NPP increases of 30% or more occurred across the continent from 1982 to 1998.  During this period, the atmosphere's CO2 concentration rose by 25.74 ppm, as calculated from the Mauna Loa data of Keeling and Whorf (1998), which amount is 0.0858 of the 300 ppm that is typically used as a reference for expressing plant growth responses to atmospheric CO2 enrichment.  Hence, for herbaceous crop plants that display NPP increases of 30% in response to a 300-ppm increase in atmospheric CO2 concentration, the real-world CO2 increase experienced between 1982 and 1998 would have been expected to increase crop productivity by 0.0858 x 30% or 2.6%.  Similarly, for trees that display NPP increases of 80% in response to a 300-ppm increase in atmospheric CO2 (Saxe et al., 1998; Idso and Kimball, 2001), the expected increase in tree productivity between 1982 and 1998 would be 0.0858 x 80% or 6.9%.  Since both of these NPP increases are considerably less that the 30% or more observed by the authors, we would expect the positive impact of the aerial fertilization effect of atmospheric CO2 enrichment on the NPP of North America's vegetation to not be identifiable in their data, as other factors were obviously even more influential in stimulating productivity over this period, in some instances by more than an order of magnitude, in fact.

This is also the conclusion of the authors, who enumerate a number of growth-promoting factors whose individual effects in some cases and combined effects in others must have greatly overshadowed the CO2 aerial fertilization effect in different regions of the continent in different years and at different times of the year.  Some of the factors they mention are increased precipitation during summer, increasingly intensive crop and forest management, increasing use of genetically improved plants, the regrowth of forests on abandoned cropland, improvements in agricultural practices such as irrigation and fertilization, and warming that lengthens the growing season.  There are also growth-retarding factors that may have come into play in some areas, such as declining precipitation in places such as the American Southwest, decreasing temperatures at high latitudes, and increasing concentrations of tropospheric ozone and acid deposition, which in some cases could easily overpower the CO2 aerial fertilization effect and lead to localized decreases in NPP, which were in fact observed in some instances.

What it means
A large number of factors of both natural and anthropogenic origin combine to determine the productivity of earth's vegetation.  In North America between 1982 and 1998, these factors varied in ways that produced an overall continent-wide NPP increase on the order of 30%.  Imbedded in that NPP increase was the effect of the concurrent rise in the air's CO2 content, which likely accounted for anywhere from 8.7 to 23% of the total absolute increase (2.6%/30% = 8.7% and 6.9%/30% = 23%).  As time progresses, however, we would expect climatic effects to periodically change direction and, hence, have much smaller cumulative long-term impacts on global NPP, so that the positive effect of the continuing rise in the air's CO2 content would play an increasingly greater and relatively more important role in stimulating the planet's productivity.  Such is also likely to occur with respect to man's genetic manipulation of earth's vegetation and his application of best management practices to both natural and agro-ecosystems.

References
Idso, S.B. and Kimball, B.A.  2001.  CO2 enrichment of sour orange trees: 13 years and counting.  Environmental and Experimental Botany 46: 147-153.

Keeling, C.D. and Whorf, T.P.  1998.  Atmospheric CO2 Concentrations - Mauna Loa Observatory, Hawaii, 1958-1997 (revised August 2000).  NDP-001.  Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Saxe, H., Ellsworth, D.S. and Heath, J.  1998.  Tree and forest functioning in an enriched CO2 atmosphere.  New Phytologist 139: 395-436.