The oil serves a few purposes that are important.
Firstly it helps to avoid it sticking, although if you grill at a high enough temperature that isn't a problem. Also, if you lift a steak 20 seconds after putting it on the pan, and then put it down again, it will have formed enough of a moisture layer on the surface to avoid it sticking. That's an old chef's trick.
Secondly, oil helps to evenly coat and spread your season when it cooks. It also helps your seasoning to "stick" to the meat and even penetrate deeper when cooking.
Thirdly, fat is a distributor of flavour in your mouth. The oil helps to distribute the flavours over more taste buds which ups the flavour according to new science coming out of Ferran Adria's kitchen.
Lastly, the oil helps to sear a crust on to the steak which you cannot get without oil, or at least without overcooking your steaks.
So the oil does serve more purposes than simply helping it not to stick...
The method I mentioned was achieved from past experimentation.
I have no sticking issues. Like you said if you leave it for a short while it will not stick.
Seasoning stays put.
I find the fat in/on the steak more than enough to coat the pan. Whatever is left after cooking I pour back over the steak while it rests on a warm cutting board.
I get a nice 'crust' without the oil.
I've tried with and without oil and I prefer the result I get without oil. The rumps I do I find better than restaurant rumps, full of flavour, melt in your mouth soft and others tend to agree (hope they are not just being polite).