Marcus, yep, the research focuses on C3 plants, which include wheat, rice, and soybeans. Unfortunately all trees are also C3 plants, as are ~85% of plants on the planet. C3 designation has to do with the Calvin cycle and how the plants fix carbon during photosynthesis.
As I mentioned, they did control for soil quality, mineral content, etc. and used wild plants and heirloom strains to control for some of the issues you mentioned, such as genetic modifications, etc. The FACE methodology is the gold standard for isolating CO2 as a variable so data indicates that this effect is independent from the problems we see from soil depletion, selective breeding for commercial traits, etc. Those things are known problems, what I am getting at here is that increasing atmospheric CO2 is an additional factor which exacerbates those problems and which as permaculturists we are not necessarily "safe" from just because we are forest gardening on healthy soils, for instance.
I agree with you on things like spinach, which is why I mentioned leafy greens in my original post as a potential workaround. Unfortunately very few people in this world get the bulk of their calories from spinach, and the implication of this research is that <em>even for plants grown in a permaculture setting</em>, the micronutrient content and ratio of protein to carbohydrate of a diet consisting of a given number of calories will gradually decline with rising CO2 levels unless the proportions of verious plants in the diet changes. I agree with you that it's basically a dilution effect (like food coloring in water), which means that you must consume ever more calories to get the same amount of nutrition, if all other factors hold steady. This is not ideal, which is why I suggested increasing consumption of very low-calorie foods such as teas/tisanes and leafy greens to compensate.
I also think this has a lot of future research potential, such as: What food plants do not respond in this manner to increasing CO2 levels or do so only minimally (possibly C4 or CAM plants) and does it make sense to grow more of them? How can we feasibly select for plants that take up and store increased amounts of micronutrients, protein, etc.--is this even possible on the home scale? Does the CO2 effect have implications for pest predation (micronutrients are often natural pesticides and sugars often attract pests)?