It does stave off hunger. Think of your stomach as a big balloon. It can only hold a given volume. Fiber expands when it mixes with the liquids in your stomach, thus filling you up sooner. There are receptors on the inside of the stomach wall that send signals to your brain telling it when you are full. Basically, when you think you're full, you're full.
In my example above I noted that I use Flaxseed as my source of fiber. To claim that this has no nutritional value is flatly false. The fiber in it will help to regulate your insulin levels which helps to control how quickly energies are burned up, with sugars being the quickest. It's also good for your digestive system. The flaxseed itself contains a lot of Omega-3 which helps you in a variety of ways: lowers blood pressure, lowers LDL cholesterol levels, helps reduce arterial plaque. It contains something called Lignans which contain antioxidant properties.
Flaxseed is one of the healthiest things you can consume.