The goal of a humane government structure should be to defend people and itself from abusive forms of power. Those cartels are analogous to (inhumane) government. They, as a result of US policy, have gained the ability to supersede previous governmental structures by using sheer force. They became dictatorial regimes. Conversely, private businesses acting as "corporations," as far as the US is concerned, are only powerful because of the system of government. The system inherently lends itself to corporatism through an architecture that allows for overreach at the very foundation of its design.
I don't mean to mince words again but I have to, for the sake of liberty activists who try, fail, and sometimes succeed. Power is something we can reject. We can do it individually and collectively. (I realize we're using different interpretations of the word "reject" but it's still a point.) Knowledge and civil disobedience are often options. If physically freeing oneself is unwise or nearly impossible, one may try to stay mentally free. Rejection begins with mentality. If we don't perpetuate the philosophy and beauty of liberation, of rejection over defeatism, then I worry that this 'eternal flame,' which sparks the struggle for freedom and pervades a yearning for individuality and truth, may grow too dim.
No, I know, the practicality of your words about power ring true. There are forms of power so hard to reject, physically and mentally, that they effectively render a person, or millions of people: powerless.
I'd say the Mexican drug cartels are de-facto examples of private corporations when they don't or can't rely on government to give them their power.