I've seen the technique of using the knife to rotate the pit, but I don't really do it because I'm generally happy with radial pieces so cutting the pit half into quarters isn't a problem. I also just generally have one avocado at a time, so I'm not going for speed (as one would say making guac).

But my point was that unless you actually slice the pit in half, neither half is going to have a flat face that you can put on a plate of oil or whatever. Rather one half is going to have the pit sticking out, and the other half is going to have a pit shaped indentation that doesn't touch the oil.