While I'm not sympathetic to prison operators or the mass-incarceration system in general, this is a weak article with little substance. Declaring an assertion to be myth requires a substantial investment in disproving it. Indeed, there is not a single fact presented in opposition to what is perhaps the most important myth #1. It is possible (or damned well ought to be, and if it isn't, then that's a cause of action by itself) to account for exactly what the government and inmates are paying. Someone who makes a concerted effort to figure out what that is would be a top-notch investigative reporter. Someone who writes "Does anyone actually have proof of this? Seriously, is anyone sure that this happens?" is either ranting or a hack. When you write an article asserting that a political opponent's views are myths, you take on the burden of proof. Simply asserting (without even a reference) that no one has proven the opposite doesn't cut it, even if that's true.
There are similar problems with the other "myths", such as attempting to rebut the notion that private prison operations have limited influence by showing a graph of private prison populations (one that, I might add, doesn't exactly bolster the case). So what? If 8% (or 20% or X%) of prisoners are in private prisons, how does that affect their influence on incarceration as a policy? If that rate is different in various states, can you connect the differences with the kind of policy influence you expect to find? That's legwork. That's investigative reporting.
Anyone who would like to see significant prison reform deserves, and needs, much better than this. If this were truly a reflection of the prison reform movement's best arguments, it's small wonder it's not having much success.