I don't generally consider myself a conspiracy theorist, but I agree with the previous comment. For-profit prisons not only make money by having more prisoners staying for longer, but in many cases have actually been required to maintain a minimum number of prisoners. That creates a huge incentive to the operators of private prisons to make sure that people are sentenced to terms that are as long as possible, and to make sure that as many people as possible are given sentences that get them into those prisons vs. alternatives like house arrest, community service, court-ordered rehabilitation meeting attendance, etc.
I think it would be pretty naive to assume that private actors can have no influence over an unelected/appointed judiciary anyway, but don't forget that many places in the United States have an elected judiciary that needs to campaign every few years to maintain their status, which clearly opens them up to influence by those prisons.