Some say integrity is fundamental flaw of our nature. That is, the human nature.
Well assume that you are an alien, a being who has no prior knowledge of this world, of our world. And assume that you have decided to take a look at our this existence. Wanting to figure out how things work here and why they do so, a kind of extraterrestrial anthropologist.
Having spent some time on earth you find out that there are a bunch of seemingly working societal structures, leaders, laws, commerce and so on. You also note that humans in general share common values and principles (equality, humanity, impartiality etc.). And these transcend across all aspects of human life.
You notice however that there is also great suffering on earth. People dying needlessly each and every day from various number of causes. But shockingly the larger part of this suffering is self induced i.e. man-made. And the minority of the human population who are actually doing well are the ones at the very top of the structures you noticed earlier. The leaders, trend-setters, decision makers, organizers, and what have you.
You start wondering why this is.
Going over what you found you start asking questions. “So they all follow structures which are supposedly based on the common human principles right? But how is it possible then that such a large majority of humans suffer whilst the others live in bliss? Do the common principles extend to everyone?”
You conclude that the people at the very top of the structures must have compromised their integrity to achieve their goals in the wake of all the misery around them. Because how else can you have so much power and influence and yet so much suffering? What is more concerning is the common association of power with integrity. The idea that with more power comes more responsibilities. And in the case of humans, you have a society with leaders (in whatever context or capacity) who enforce the concept of integrity to their subjects whilst mostly ignoring it themselves.
Therefore you summarize that integrity is a flaw of human nature because of those that are able to disregard it.