“Fiber” as a dietary term refers to plant material that humans can’t digest. Some (edible parts of) plants have more of it than others; for instance, lentils contain about eight times as much fiber per unit of weight as potatoes do. “Plants contain fiber” is about as accurate a statement as “plants contain vitamins”; not all of them contain it in equal measure.

It’s not that hard to construct a diet that is rich in plants but low in fiber, especially if you include plant-based foods like tofu, which can contain even less of it.