All olives are processed, one way or another. Off the tree, they're full of oleuropein, a spectacularly bitter substance making them all but inedible. Fortunately, oleuropein is water soluble, and soaking in salt water or a solution of lye leaches it out - and the techniques go back into antiquity, at least as far as the Achaean Greeks.
That said, EVOO is the *least* processed olive oil. The descending grades pretty much correspond to the amount of processing, with pomace (chemical extraction) at the very bottom.
The challenge with EVOO is making sure that that's what you've actually got. In the US, at least, we have a problem with counterfeit EVOO, particularly that marked as being from Italy.