Probably, people who say that fiber is filling are speaking in relative terms. Sugar and starch--which are very digestible--can cause your blood sugar to spike and then drop one to three hours later, making you hungry. (Starch is the old fashioned name for those wonderful complex carbohydrates we're constantly told are good for us. It's the same thing that in bygone days, people avoided, along with sugar, to lose weight.) Nevertheless, I don't see how something that's indigestible fills you up in the first place.
What is filling? Fat and protein. Fat also makes vitamins D, E and K and beta carotene (the last two of which are found in foods like broccoli and salad) absorbable by your body. Go ahead and have the broccoli with some butter or cheese sauce and put the full-fat dressing on the salad. And have something with protein while you're at it. You'll be less likely to visit a vending machine later.
Another thing I'm finding filling is nutrients. Since I started my cavity-healing diet where I substituted more nutritious foods like sardines, liver, marrow and cream for some less nutritious (but low carb) foods, I find I'm less hungry than before. These stepchildren of the food world are packed with a lot more nutrients than anything you'll find in the produce section, and some of the nutrients are better absorbed. I've been making a lot fewer Kind Bar and diet soda runs at work since I started eating more of these foods. Yes, some of these are an acquired taste. But since changing my diet and learning different ways of preparing these foods, I find I like them well enough to keep eating them. The sardines in particular are satsifying. I'll be halfway through eating a can of them when I suddenly feel wonderful. Maybe it's the high Omega-3 content.
My father wasn't opposed to broccoli, but here's something he really would say after a day spent working construction: "Betty, let's have liver for dinner."