That is mainly, but it does a host of other things. When the chain goes around a corner (sprocket/tip of bar) it must rotate and the oil supports that action (as you stated). There are several layers that rotate (albeit only a bit) during that process and lots of oil is required to creep in there and protect all those layers. But also remember that as the chain slides along the length of the bar, the side links are sliding on the guide rails. This is a basic and highly deleterious friction source - and the chain oil is probably most useful here in the short term of a chain/bar's life. If you have ever had a bar with burn marks along the "bottom" that is usually from poor oiling or poor oil. Those parts do not turn, ever. As you bear into the wood (either the hard way, or camming in using the dogs), this friction is only exacerbated. There is a small benefit from rust prevention, but that usually only comes into play if you work in the rain/snow, or so seldom that your chain dies from sitting, rather that working.
Probably the largest advantage to good oil vs cheap oil is the tackifiers and anti-slinging additives. They hold the oil in the right spots so that it can do its work.
All in all, you may do the most to help yourself by turning over your bar often, keeping the chain sharp (it reduces life, but helps out your saw and the work it does in a HUGE way), and repairing or replacing worn stuff ASAP. Chainsaws are generally pretty cheap considering the work they do, so I don't hesitate to switch out a bar or chain if it is holding me back. I buy primarily used professional saws, and some TLC the day I get them home will result in mountains of effort saved for very little money. I buy ultralight and pro-light bars and I just keep on cutting wood. I struggle to walk, start the bigger saws, and bend over to pick up the wood, and I can't destroy a tree as fast as I used to, but a combination of a good light saw, a light bar, and a sharp chain has kept me in the woods at least 5 years longer than I have a right to be. I am actually not as old as that suggests, but I had a fall a couple decades back, and my joints have completely given up on their end of the bargain.