At the risk of stretching the metaphor - fat is useful, too. In animals, a layer of fat will help you withstand 'lean times' of less nutrition or higher work. Run the body too hard without fat, and you burn muscle for short-term gain, or worse, die.
Similarly, in organizations, 'fat' helps out when the workload increases or productivity decreases. Run an organization too lean, and when you need to respond to a new situation, you burn out your muscle (workers) and/or go broke. This is similar to the concept of "slack."
The metaphor extension is valid. If they had succeeded in just cutting fat, it might have been merely a mistake -- failing to understand how redundancy works in an organization.
Instead, they cut without regard to fat content. Many of the organizations were already operating on a shoestring. We didn't have an abundance of park rangers. It wasn't "merely" a mistake. It was the application of ideology, without regard to either the principles of good governance or the law.
...said no junior associate at a private equity firm ever.