There are people I know and trust who say they can taste the difference in grass-fed beef and free-range chickens. That said, from what I have seen, the higher quality comes from many factors, not just the "organic" management. More care, better food. But, let's face it, it is much more expensive to produce. And everyone has to eat. That might not be a concern for you, but others worry about it.
One, that simply is not true. They use "organic" pesticides, some which can be as harmful as "conventional" controls. Also, organic production doesn't mean that the produce is handled in the shipping or the retail environment safely.
But, more to the point, it is irresponsible to imply that organic produce does not need to be washed. This is the kind of strawman argument organic fans put forth that distracts us from spending real money and energy on real problems.
Example: The toxins in the processed peanuts that sickened many and said to have killed several people had nothing to do with pesticides and everything to do with the handling.
Common sense would tell you to wash all fresh produce. The hands of the people handling it can shovel real bacteria that can make you real sick, not to mention flies.
Household hygiene isn't the only thing that suffers when the focus is moved from where it should be. All totaled, the organic movement has done more harm than good.