If someone wants to argue that the public ownership of a housing project somehow conveys rights to its occupants that they otherwise wouldn't have, then these housing projects should be treated no differently than a park or public street. Nobody should be allowed to lock their doors, and the public should be able to enter the apartments whenever they feel like it.
Actually, the private individual has the ability to negotiate and if the terms aren't to his liking he can go down the road and shop for a better price or better terms.
Some of the PHAs have long waiting lists and often have a "take it or leave" option for the tenant; it's this property right now or lose your place on the list. They have no ability to negotiate or find other options and few other options outside of a cardboard box in the alley.