Directly from the study you linked, one sentence below your quote above:
"One possible solution is using a small amount of green light. To test this hypothesis,
Kim et al. (2004a) grew lettuce plants under red and blue LEDs with and without 5% (6 μmol·m−2·s−1) green from LEDs with both treatments at the same total
PPF (136 μmol·m−2·s−1). They observed no impact on lettuce growth with all measurable characteristics such as photosynthesis rate, shoot weight, leaf area, and leaf number being the same with and without green. "
They had to increase green to 24% of the overall light output before they had any increase in biomass at all.
Don't get me wrong, I'm not saying that there isn't a need for whites to hit additional accessory pigments. However, we are attempting to increase efficiency and reduce power consumption. If I have to add 24% of my overall power into green to get ANY return, I just wasted a lot of money and power for very little in return. The use of that study simply isn't worth linking anymore. They used diodes that were less than 20% of the efficiency of current diodes (of all colors and whites) and relied heavily on data from prior studies that used filters and not discrete diodes.
Here is a link to the study they used in your link
http://aob.oxfordjournals.org/content/94/5/691.full (notice that all but 4 of their resources are from the 1990's thru the 1970's)
When we read data from these studies, we need to remember a few things: Do not take them out of context. Don't stop reading after we find a sentence that meets our goals. Understand the limits of their test. The resources they site usually have the more detailed information. Last but not least, who paid for the study and how might that have skewed the results (and it nearly always does).
One question from me: Has NASA started their second round of lawsuits on companies claiming to have worked for and with them on light development when all they actually did was submit to be used in a trial? (cough AT cough)