Does it matter? It is the inmates and their family who get scammed in the end.
Arguing between "oh is it the government, or the market? don't know let's have a long discussion about it". The article clearly shows there isn't much of a separation between. These companies (in this case single company) is heavily lobbying and bribing government officials with kickbacks and such tricks.
I wouldn't be surprised that when some prison official retires she/he gets to work as a "consultant" for JPay.
Hell, these people are infants compared to what is going on in the rest of the industries -- military, healthcare, agrobiz, telecoms.
Repeat after me "the there is no effective difference between the governmental agencies and the large companies and conglomerates". It is the same people just playing musical chairs. FDA chairman worked for Monsanto (as an example). Ex procurement general works for Northrop Grumman and so on.
Objectively, can anyone say that isn't a rational outcome of a the "free market"? I can't. The best and easiest way to turn a profit at that scale is regulatory capture. A few millions in bribes have a chance of getting back billions in profits in the future.