I am an organic grower. We've managed our small farm organically for the last 5 years. We raise goats, a few pigs, chickens, garden vegetables and some fruit for sale at farmer's market. Actually, we're even beyond organic. We have a philosophy here of "if you can't eat it, you can't spray it." So I don't even use organically approved stuff like pyrethrum. Here's my take on the whole thing.
I think there's a huge amount of woo in the organic movement, however, I don't think it's all woo. I think most of the woo comes from organic consumer devotees rather than actual growers. I think they tend to read a piece of information or a study, then make illogical leaps based on the information. Then these mythical assumptions get passed around like gossip and are believed to be true. This "organic farmers will plant root vegetables to clean the soil from pesticides" smacks of this "myth phenomenon" to me. I know of no organic farmers that do that. They grow carrots because they are in an agricultural area that can grow good carrots, they have good deep topsoil, and because they have a market for them. Period. Good quality carrots are actually somewhat difficult to grow, so no one would do it for a non-profitable reason.
It is true that root crops tend to have more soil persistent pesticide residues in them than above ground crops. DDT and chlordane, both of which have been banned for decades are still being found in trace amounts on root vegetables, even organic ones.
http://www.chemistry.org/portal/a/c/s/1/feature_pro.html?id=c373e908bdb566e18f6a17245d830100
There are many good sound practices espoused by organic growers that are being carried over into "traditional" farming recommendations. As well as being a farmer, I am an active Master Gardener, so I spend a good deal of my time at the county extension office dispensing advice and information to local residents. If you look through most of the recommendation publications coming out of extension offices now vs 5 years ago, you will see a definite trend of advising less chemical control of various problems and more cultural control. The basic science behind organic methods is indeed there, in many cases.
Here's my opinion about the whole "nutritionally dense" thing. Freshly picked vegetables have more nutrients in them than less fresh vegetables. Sugars start breaking down into starches, and vitamins, particularly vitamin C, are lost the longer the produce stays on shelf. It's not a whole lot, though. This link says it's around 10%, normally.
http://www.mydna.com/wellness/nutrition/scoop/nutrition_food_organic_vegetables.html
So, I think it would be relatively easy to "prove" that organic veggies were more "nutritionally dense" than typical supermarket veggies, if the researchers purchased the organic produce directly from the farm, or from say at a farmer's market, and got their conventionally grown produce from the average supermarket. What they would actually be proving, though, is that fresher produce has more vitamins in it than older produce.
Even choosing between organic and conventional foods from the same supermarket, the organic veggies are probably fresher. Conventional produce can be sprayed with antibacterial agents and stronger cleaners than organic processors are permitted to use, so conventional produce, in general lasts longer on the shelves than organic does. So, in general, the organic produce at the store has more frequent deliveries and a shorter farm to market time than the conventional.
If the research were between freshly picked produce of both types of farming methods, of the exact same variety of vegetable, in similar growing conditions, my personal bet is that there would be very little, if any, measureable nutritional difference between the two.
Just my two cents
Meg