The source linked to the claim contains a quote from a WSU press release that states, “consumers who switch to organic fruits, vegetables, and cereals would get 20 to 40 percent more antioxidants. That’s the equivalent of about two extra portions of fruit and vegetables a day, with no increase in caloric intake.” (WSU Insider) This is meant to prove that organic produce and cereals are “healthier” than conventional ones, simply because they increase the portions of fruits and vegetables per day. If someone is eating the full recommended portion of fruits and vegetables per day, an extra 40% of fruit could lead to a spike in sugar levels, and overtime even cause cravings for more sodium and processed "unhealthy" foods. This makes this quote alone unconvincing and still doesn’t prove organic foods are healthier.
Organic foods that have lower amounts of pesticides in them are technically “safer” to eat than conventional foods, but that doesn’t in turn make them healthier. A quote from the National Library of Medicine says this about research done on the correlation between eating organic food and a benefit on human health: “Few clinical trials assessed direct improvements in health outcomes associated with organic food consumption; most assessed either differences in pesticide exposure or other indirect measures.” (NIH) All of these claims made to try to convince us that organic food is healthier actually just tells us that we will be consuming more sugar and might have a lower risk of being exposed to pesticides. If these companies were simply claiming that eating organic foods decreased your risk of exposure to chemicals and pesticides and increased your fruits/vegetable intake, the overall claim wouldn’t be so stark or incorrect.
The same source from the NIH states “there appears to be little variation between organic and conventional food products in terms of macro nutritional value.” The only “benefits” they are detecting in these studies are increased antioxidants and the researchers themselves also state that these findings have not been proved to be statistically significant or have an impact on human health. It's not to say that organic food might not have benefits or separate benefits from conventional foods, but the general statement that it is “healthier” is exaggerated and misleading.