What I've been told is that there is a synthetic pesticide that's approved for organic farming because it breaks down completely before the food makes it to market, leaving no residue. It's not used much at all in conventional farming due to its expense.
This is the first I've heard, ever, of any controversy over "organic pesticides". I'll look into it more, but I have to say I'm skeptical, because I've seen a lot of anti-organic propaganda and no one even mentioned this angle.
As for the pesticide residue issue, I think it's a strong claim of fraud to assert that every study or summary of studies that found lower "pesticide residues" is really only referring to a specific type of pesticide in order to mislead the public. "Organic pesticide" wouldn't be the correct phrase, in any case, when referring to a pesticide considered appropriate for organic farming. The word would be natural. Many synthetic pesticides are organic molecules. DDT is an organic pesticide, for instance.
Ok, I just read the Ars Technica article and I have to take issue with the terminology as well as the way the author didn't note that the issue here isn't so much a matter of organic production being equivalent to conventional production but rather it's about specific pesticides used. People should not call pesticides "organic pesticides" unless they're talking about the chemical (organic versus inorganic). "Pesticides commonly used in organic farming" may be a lot to say, but that's accurate.
And, of course, it's true that simply because something is natural doesn't mean it's safer than something synthetic. But, that doesn't mean other aspects of organic farming don't matter and the apparent fact that one type of pesticide used in organic farming is not ideal. Some organic farmers don't use chemical pesticides.
Studies have found lower "pesticide residues" (I doubt they were lying by only considering synthetic organic pesticides and not specifying that) on organic produce and higher vitamin/mineral content.