No, you don't have to go through II.
Marriott is affiliated with II. There are a few older Marriotts that trade through both RCI and II, but most trade only through II. That doesn't stop you from using one of the independent exchange companies. However, they are much smaller and generally don't have anywhere near as much available inventory as II.
Phrased differently, once you reserve the floating week that you own, you can do almost anything you want with it. You can occupy it, you can rent it to someone else, you can rent it through Marriott (if Marriott will accept it), you can let a friend or relative use it, you can exchange it through II, you can exchange it through a smaller independent exchange company or you can exchange it directly with another timeshare owner that you find. Or if you buy directly from Marriott, you can exchange the use of the week for Marriott Rewards points.