I don't think mixing the Peter principle with the advancement offered through unethical work offers more insights than both alone.

Really feels shoehorned in.

I don't know how accurate the description in TFA is, but it seems to me it's stating the petered employee, if they are self-aware enough to notice the corner they find themselves in, and desperate that their career is at stake, is more likely to turn to unethical paths in order to become valuable to the leadership. That's the connection.