I recently lived nearly two years in a new CIHA apartment building.  First, it's not entirely true that they are "private sector."  Where do you think the rent subsidies come from? Not from CIRI's benevolence, but from the federal HUD, and from Alaska Housing Finance Corporation.  

Re: your "people they deem worthy" comment, it's true they do have a very thorough background check process for rental applicants. IMO, this is a quite valid part of the process, that essentially verifies income, and weeds out the deadbeats and troublemakers who could be a danger to other residents.