We shouldn't assume that because we are a great ape that we eat the same as other great apes. Humans spent two million years away from the jungle evolving in the savanna, with very different food sources. Our guts changed quite a bit in that time, and our digestion doesn't work the same.
Their is no doubt that for millions of years the humans have eaten much less fiber than their ape ancestors.
You just have to look to the belly of a healthy, non-obese human and compare it with the bellies of the apes. The bellies of the apes are much bigger, despite not having the fat of humans, because they have much longer intestines, which are packed in there, which are required for the fermentation of the large amount of fiber included in their diets.
The intestines of humans are not so reduced as those of the obligate carnivores, but they are still much shorter than of most apes or monkeys.
Our health is still dependent on eating a decent amount of "fiber", but the amount we need is not comparable with what an ape needs.
