How important is washing produce? It seems to me that you don't need to wash vegetables you're going to peel. If toxins are on the surface, peeling solves the problem; if toxins have been absorbed into the flesh of the vegetable, washing won't help.

Is that right, or am I missing something?
First, I always rinse produce well with tap water even before putting it into the refer. I grew up on a farm and witnessed what it may be exposed to even when the farm hands care. I would also wash anything that is being peeled as the peeling process requires--at least for me--my fingers to touch the peeling, and then the peeled veggie as I am peeling the rest of it.