Extra Virgin Olive oil is quite a different animal from the various vegetable oils out there, and is in keeping with his diet. I use olive oil for salads, and coconut oil in cooking, and butter on veggies.
To the other points you raise - one can eat lots of greens and certain other vegetables. Fruits are not essential to our health, though hard to give up. When I am on the low side, blood sugar-wise, I do have raisins, prunes, grapefruit, or whatever is available, instead of the more scientifically proven glucose tablets.