Yes, but even state and federally owned prisons use an army of specialized contractors for much of their staffing and supplies. Since many of those companies were established specifically to service prisons it creates the same incentives to spend large amount of money lobbying for harsher sentences and other policies that grow the prison industry in general. It's not much of a concern for, say, Tyson, which is so big that prisons are a tiny part of their revenue but it's a bigger issue with other services.

The fully privatized prisons are on a whole other level of messed up.